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MATHEMATICS (706 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 27)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 6)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 3)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 5)
Advances in Science and Research (ASR)     Open Access   (Followers: 4)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 10)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Communications in Mathematical Physics
  [SJR: 1.76]   [H-I: 101]   [2 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0916 - ISSN (Online) 0010-3616
   Published by Springer-Verlag Homepage  [2352 journals]
  • Quantitative Uniform Propagation of Chaos for Maxwell Molecules
    • Authors: Roberto Cortez; Joaquin Fontbona
      Pages: 913 - 941
      Abstract: We prove propagation of chaos at explicit polynomial rates in Wasserstein distance \({\mathcal{W}_{2}}\) for Kac’s N-particle system associated with the spatially homogeneous Boltzmann equation for Maxwell molecules. Our approach is mainly based on novel probabilistic coupling techniques. Combining them with recent stabilization results for the particle system we obtain, under suitable moments assumptions on the initial distribution, a uniform-in-time estimate of order almost \({N^{-1/3}}\) for \({\mathcal{W}_{2}^{2}}\) .
      PubDate: 2018-02-17
      DOI: 10.1007/s00220-018-3101-4
      Issue No: Vol. 357, No. 3 (2018)
  • Optimal Hardy inequalities for Schrödinger operators on graphs
    • Authors: Matthias Keller; Yehuda Pinchover; Felix Pogorzelski
      Abstract: For a given subcritical discrete Schrödinger operator H on a weighted infinite graph X, we construct a Hardy-weight w which is optimal in the following sense. The operator H − λw is subcritical in X for all λ < 1, null-critical in X for λ = 1, and supercritical near any neighborhood of infinity in X for any λ > 1. Our results rely on a criticality theory for Schrödinger operators on general weighted graphs.
      PubDate: 2018-02-26
      DOI: 10.1007/s00220-018-3107-y
  • Nonperturbative Time Dependent Solution of a Simple Ionization Model
    • Authors: Ovidiu Costin; Rodica D. Costin; Joel L. Lebowitz
      Abstract: We present a non-perturbative solution of the Schrödinger equation \({i\psi_t(t,x)=-\psi_{xx}(t,x)-2(1 +\alpha \sin\omega t) \delta(x)\psi(t,x)}\) , written in units in which \({\hbar=2m=1}\) , describing the ionization of a model atom by a parametric oscillating potential. This model has been studied extensively by many authors, including us. It has surprisingly many features in common with those observed in the ionization of real atoms and emission by solids, subjected to microwave or laser radiation. Here we use new mathematical methods to go beyond previous investigations and to provide a complete and rigorous analysis of this system. We obtain the Borel-resummed transseries (multi-instanton expansion) valid for all values of α, ω, t for the wave function, ionization probability, and energy distribution of the emitted electrons, the latter not studied previously for this model. We show that for large t and small α the energy distribution has sharp peaks at energies which are multiples of ω, corresponding to photon capture. We obtain small α expansions that converge for all t, unlike those of standard perturbation theory. We expect that our analysis will serve as a basis for treating more realistic systems revealing a form of universality in different emission processes.
      PubDate: 2018-02-22
      DOI: 10.1007/s00220-018-3105-0
  • The Full Ward-Takahashi Identity for Colored Tensor Models
    • Authors: Carlos I. Pérez-Sánchez
      Abstract: Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank-D interactions including, but not restricted to, all melonic \({\varphi^4}\) -vertices—to wit, solely those quartic vertices that can lead to dominant spherical contributions in the large-N expansion—the aforementioned boundary graphs are shown to be precisely all (possibly disconnected) vertex-bipartite regularly edge-D-colored graphs. The concept of CTM-compatible boundary-graph automorphism is introduced and an auxiliary graph calculus is developed. With the aid of these constructs, certain U (∞)-invariance of the path integral measure is fully exploited in order to derive a strong Ward-Takahashi Identity for CTMs with a symmetry-breaking kinetic term. For the rank-3 \({\varphi^4}\) -theory, we get the exact integral-like equation for the 2-point function. Similarly, exact equations for higher multipoint functions can be readily obtained departing from this full Ward-Takahashi identity. Our results hold for some Group Field Theories as well. Altogether, our non-perturbative approach trades some graph theoretical methods for analytical ones. We believe that these tools can be extended to tensorial SYK-models.
      PubDate: 2018-02-22
      DOI: 10.1007/s00220-018-3103-2
  • The q -AGT–W Relations Via Shuffle Algebras
    • Authors: Andrei Neguţ
      Abstract: We construct the action of the q-deformed W-algebra on its level r representation geometrically, using the moduli space of U(r) instantons on the plane and the double shuffle algebra. We give an explicit LDU decomposition for the action of W-algebra currents in the fixed point basis of the level r representation, and prove a relation between the Carlsson–Okounkov Ext operator and intertwiners for the deformed W-algebra. We interpret this result as a q-deformed version of the AGT–W relations.
      PubDate: 2018-02-21
      DOI: 10.1007/s00220-018-3102-3
  • Dimension of the SLE Light Cone, the SLE Fan, and $${{\rm
           SLE}_\kappa(\rho)}$$ SLE κ ( ρ ) for $${\kappa \in (0,4)}$$ κ ∈ ( 0 ,
           4 ) and $${\rho \in}$$ ρ ∈ $${\big[{\tfrac{\kappa}{2}}-4,-2\big)}$$ [
           κ 2 - 4 , - 2 )
    • Authors: Jason Miller
      Abstract: Suppose that h is a Gaussian free field (GFF) on a planar domain. Fix \({\kappa \in (0,4)}\) . The \({{\rm SLE}_\kappa}\) light cone L \({(\theta)}\) of h with opening angle \({\theta \in [0,\pi]}\) is the set of points reachable from a given boundary point by angle-varying flow lines of the (formal) vector field \({e^{ih/\chi}}\) , \({\chi = \tfrac{2}{\sqrt{\kappa}} - \tfrac{\sqrt{\kappa}}{2}}\) , with angles in \({[-\tfrac{\theta}{2},\tfrac{\theta}{2}]}\) . We derive the Hausdorff dimension of L \({(\theta)}\) . If \({\theta =0}\) then L \({(\theta)}\) is an ordinary \({{\rm SLE}_{\kappa}}\) curve (with \({\kappa < 4}\) ); if \({\theta = \pi}\) then L \({(\theta)}\) is the range of an \({{\rm SLE}_{\kappa'}}\) curve ( \({\kappa' = 16/\kappa > 4}\) ). In these extremes, this leads to a new proof of the Hausdorff dimension formula for \({{\rm SLE}}\) . We also consider \({{\rm SLE}_\kappa(\rho)}\) processes, which were originally only defined for \({\rho > -\,2}\) , but which can also be defined for \({\rho \leq -2}\) using Lévy compensation. The range of an \({{\rm SLE}_\kappa(\rho)}\) is qualitatively different when \({\rho \leq -2}\) . In particular, these curves are self-intersecting for \({\kappa < 4}\) and double points are dense, while ordinary \({{\rm SLE}_\kappa}\) is simple. It was previously shown (Miller and Sheffield in Gaussian free field light cones and \({{\rm SLE}_\kappa(\rho)}\) , 2016) that certain \({{\rm SLE}_\kappa(\rho)}\) curves agree in law with certain light cones. Combining this with other known results, we obtain a general formula for the Hausdorff dimension of \({{\rm SLE}_\kappa(\rho)}\) for all values of
      PubDate: 2018-02-20
      DOI: 10.1007/s00220-018-3109-9
  • A Cohomological Perspective on Algebraic Quantum Field Theory
    • Authors: Eli Hawkins
      Abstract: Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of constructing interacting QFT models. Symmetry is the primary tool for understanding the structure and properties of a QFT model. This perspective leads to a generalization of the algebraic quantum field theory framework, as well as a more general definition of symmetry. This means that some models may have symmetries that were not previously recognized or exploited. To first order, a deformation of a QFT model is described by a Hochschild cohomology class. A deformation could, for example, correspond to adding an interaction term to a Lagrangian. The cohomology class for such an interaction is computed here. However, the result is more general and does not require the undeformed model to be constructed from a Lagrangian. This computation leads to a more concrete version of the construction of perturbative algebraic quantum field theory.
      PubDate: 2018-02-15
      DOI: 10.1007/s00220-018-3098-8
  • Active Spanning Trees with Bending Energy on Planar Maps and SLE-Decorated
           Liouville Quantum Gravity for $${\kappa > 8}$$ κ > 8
    • Authors: Ewain Gwynne; Adrien Kassel; Jason Miller; David B. Wilson
      Abstract: We introduce a two-parameter family of probability measures on spanning trees of a planar map. One of the parameters controls the activity of the spanning tree and the other is a measure of its bending energy. When the bending parameter is 1, we recover the active spanning tree model, which is closely related to the critical Fortuin–Kasteleyn model. A random planar map decorated by a spanning tree sampled from our model can be encoded by means of a generalized version of Sheffield’s hamburger-cheeseburger bijection. Using this encoding, we prove that for a range of parameter values (including the ones corresponding to maps decorated by an active spanning tree), the infinite-volume limit of spanning-tree-decorated planar maps sampled from our model converges in the peanosphere sense, upon rescaling, to an \({{\rm SLE}_\kappa}\) -decorated γ-Liouville quantum cone with \({\kappa > 8}\) and \({\gamma = 4/ \sqrt\kappa \in (0,\sqrt 2)}\) .
      PubDate: 2018-02-14
      DOI: 10.1007/s00220-018-3104-1
  • Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator
    • Authors: Moritz Doll; Oran Gannot; Jared Wunsch
      Abstract: Let H denote the harmonic oscillator Hamiltonian on \({\mathbb{R}^d,}\) perturbed by an isotropic pseudodifferential operator of order 1. We consider the Schrödinger propagator \({U(t)=e^{-itH},}\) and find that while \({{\rm sing-supp} {\rm Tr} U(t) \subset 2 \pi \mathbb{Z}}\) as in the unperturbed case, there exists a large class of perturbations in dimensions \({d \geq 2}\) for which the singularities of \({{\rm Tr} U(t)}\) at nonzero multiples of \({2 \pi}\) are weaker than the singularity at t = 0. The remainder term in the Weyl law is of order \({o(\lambda^{d-1})}\) , improving in these cases the \({o(\lambda^{d-1})}\) remainder previously established by Helffer–Robert.
      PubDate: 2018-02-08
      DOI: 10.1007/s00220-018-3100-5
  • BPS States, Torus Links and Wild Character Varieties
    • Authors: Duiliu-Emanuel Diaconescu; Ron Donagi; Tony Pantev
      Abstract: A string theoretic framework is constructed relating the cohomology of wild character varieties to refined stable pair theory and torus link invariants. Explicit conjectural formulas are derived for wild character varieties with a unique irregular point on the projective line. For this case, this leads to a conjectural colored generalization of existing results of Hausel, Mereb and Wong as well as Shende, Treumann and Zaslow.
      PubDate: 2018-02-08
      DOI: 10.1007/s00220-018-3097-9
  • Convergence of Weak Kähler–Ricci Flows on Minimal Models of
           Positive Kodaira Dimension
    • Authors: Phylippe Eyssidieux; Vincent Guedj; Ahmed Zeriahi
      Abstract: Studying the behavior of the Kähler–Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge–Ampère equations. In this article, the third of a series on this subject, we study the long term behavior of the normalized Kähler–Ricci flow on mildly singular varieties of positive Kodaira dimension, generalizing results of Song and Tian who dealt with smooth minimal models.
      PubDate: 2018-02-07
      DOI: 10.1007/s00220-018-3087-y
  • Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
    • Authors: Clay Córdova; Ben Heidenreich; Alexandr Popolitov; Shamil Shakirov
      Abstract: We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarithmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.
      PubDate: 2018-02-07
      DOI: 10.1007/s00220-017-3072-x
  • Space–Time Discrete KPZ Equation
    • Authors: G. Cannizzaro; K. Matetski
      Abstract: We study a general family of space–time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269–504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.
      PubDate: 2018-02-03
      DOI: 10.1007/s00220-018-3089-9
  • Charting the Replica Symmetric Phase
    • Authors: Amin Coja-Oghlan; Charilaos Efthymiou; Nor Jaafari; Mihyun Kang; Tobias Kapetanopoulos
      Abstract: Diluted mean-field models are spin systems whose geometry of interactions is induced by a sparse random graph or hypergraph. Such models play an eminent role in the statistical mechanics of disordered systems as well as in combinatorics and computer science. In a path-breaking paper based on the non-rigorous ‘cavity method’, physicists predicted not only the existence of a replica symmetry breaking phase transition in such models but also sketched a detailed picture of the evolution of the Gibbs measure within the replica symmetric phase and its impact on important problems in combinatorics, computer science and physics (Krzakala et al. in Proc Natl Acad Sci 104:10318–10323, 2007). In this paper we rigorise this picture completely for a broad class of models, encompassing the Potts antiferromagnet on the random graph, the k-XORSAT model and the diluted k-spin model for even k. We also prove a conjecture about the detection problem in the stochastic block model that has received considerable attention (Decelle et al. in Phys Rev E 84:066106, 2011).
      PubDate: 2018-02-01
      DOI: 10.1007/s00220-018-3096-x
  • Scattering in the Energy Space for Boussinesq Equations
    • Authors: Claudio Muñoz; Felipe Poblete; Juan C. Pozo
      Abstract: In this note we show that all small solutions in the energy space of the generalized 1D Boussinesq equation must decay to zero as time tends to infinity, strongly on slightly proper subsets of the space-time light cone. Our result does not require any assumption on the power of the nonlinearity, working even for the supercritical range of scattering. For the proof, we use two new Virial identities in the spirit of works (Kowalczyk et al. in J Am Math Soc 30:769–798, 2017; Kowalczyk et al. in Lett Math Phys 107(5):921–931, 2017). No parity assumption on the initial data is needed.
      PubDate: 2018-01-31
      DOI: 10.1007/s00220-018-3099-7
  • BPS Jumping Loci are Automorphic
    • Authors: Shamit Kachru; Arnav Tripathy
      Abstract: We show that BPS jumping loci–loci in the moduli space of string compactifications where the number of BPS states jumps in an upper semi-continuous manner—naturally appear as Fourier coefficients of (vector space-valued) automorphic forms. For the case of T2 compactification, the jumping loci are governed by a modular form studied by Hirzebruch and Zagier, while the jumping loci in K3 compactification appear in a story developed by Oda and Kudla–Millson in arithmetic geometry. We also comment on some curious related automorphy in the physics of black hole attractors and flux vacua.
      PubDate: 2018-01-31
      DOI: 10.1007/s00220-018-3090-3
  • Lozenge Tiling Dynamics and Convergence to the Hydrodynamic Equation
    • Authors: Benoît Laslier; Fabio Lucio Toninelli
      Abstract: We study a reversible continuous-time Markov dynamics of a discrete (2 + 1)-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the \({L\times L}\) torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in Luby et al. (SIAM J Comput 31:167–192, 2001): in terms of interlaced particles, a particle jump of length n that preserves the interlacement constraints has rate 1/(2n). This dynamics presents special features: the average mutual volume between two interface configurations decreases with time (Luby et al. 2001) and a certain one-dimensional projection of the dynamics is described by the heat equation (Wilson in Ann Appl Probab 14:274–325, 2004). In this work we prove a hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as \({L\to\infty}\) to the solution of a non-linear parabolic PDE. The initial profile is assumed to be C2 differentiable and to contain no “frozen region”. The explicit form of the PDE was recently conjectured (Laslier and Toninelli in Ann Henri Poincaré Theor Math Phys 18:2007–2043, 2017) on the basis of local equilibrium considerations. In contrast with the hydrodynamic equation for the Langevin dynamics of the Ginzburg–Landau model (Funaki and Spohn in Commun Math Phys 85:1–36, 1997; Nishikawa in Commun Math Phys 127:205–227, 2003), here the mobility coefficient turns out to be a non-trivial function of the interface slope.
      PubDate: 2018-01-30
      DOI: 10.1007/s00220-018-3095-y
  • The Sum Over Topological Sectors and θ in the 2+1-Dimensional
           $${\mathbb{CP}^1 \sigma}$$ CP 1 σ -Model
    • Authors: Daniel S. Freed; Zohar Komargodski; Nathan Seiberg
      Abstract: We discuss the three spacetime dimensional \({\mathbb{CP}^N}\) model and specialize to the \({\mathbb{CP}^1}\) model. Because of the Hopf map \({\pi_3(\mathbb{CP}^1)=\mathbb{Z}}\) one might try to couple the model to a periodic θ parameter. However, we argue that only the values θ = 0 and θ = π are consistent. For these values the Skyrmions in the model are bosons and fermions respectively, rather than being anyons. We also extend the model by coupling it to a topological quantum field theory, such that the Skyrmions are anyons. We use techniques from geometry and topology to construct the θ = π theory on arbitrary 3-manifolds, and use recent results about invertible field theories to prove that no other values of \({\theta}\) satisfy the necessary locality.
      PubDate: 2018-01-30
      DOI: 10.1007/s00220-018-3093-0
  • Rigidity for Von Neumann Algebras Given by Locally Compact Groups and
           Their Crossed Products
    • Authors: Arnaud Brothier; Tobe Deprez; Stefaan Vaes
      Abstract: We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected simple Lie groups of real rank one, the crossed product has a unique Cartan subalgebra up to unitary conjugacy. We then deduce a W* strong rigidity theorem for irreducible actions of products of such groups. More generally, our results hold for products of locally compact groups that are nonamenable, weakly amenable and that belong to Ozawa’s class \(\mathcal{S}\) .
      PubDate: 2018-01-30
      DOI: 10.1007/s00220-018-3091-2
  • Discretisation Schemes for Level Sets of Planar Gaussian Fields
    • Authors: D. Beliaev; S. Muirhead
      Abstract: Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic compact manifolds. Our work is motivated by questions about the geometry of such random functions, in particular relating to the structure of their nodal and level sets. We study four discretisation schemes that extract information about level sets of planar Gaussian fields. Each scheme recovers information up to a different level of precision, and each requires a maximum mesh-size in order to be valid with high probability. The first two schemes are generalisations and enhancements of similar schemes that have appeared in the literature (Beffara and Gayet in Publ Math IHES, 2017.; Mischaikow and Wanner in Ann Appl Probab 17:980–1018, 2007); these give complete topological information about the level sets on either a local or global scale. As an application, we improve the results in Beffara and Gayet (2017) on Russo–Seymour–Welsh estimates for the nodal set of positively-correlated planar Gaussian fields. The third and fourth schemes are, to the best of our knowledge, completely new. The third scheme is specific to the nodal set of the random plane wave, and provides global topological information about the nodal set up to ‘visible ambiguities’. The fourth scheme gives a way to approximate the mean number of excursion domains of planar Gaussian fields.
      PubDate: 2018-01-29
      DOI: 10.1007/s00220-018-3084-1
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