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  Subjects -> STATISTICS (Total: 130 journals)
Showing 1 - 151 of 151 Journals sorted alphabetically
Advances in Complex Systems     Hybrid Journal   (Followers: 11)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 62)
Annals of Applied Statistics     Full-text available via subscription   (Followers: 39)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Argumentation et analyse du discours     Open Access   (Followers: 11)
Asian Journal of Mathematics & Statistics     Open Access   (Followers: 8)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 4)
Australian & New Zealand Journal of Statistics     Hybrid Journal   (Followers: 13)
Bernoulli     Full-text available via subscription   (Followers: 9)
Biometrical Journal     Hybrid Journal   (Followers: 11)
Biometrics     Hybrid Journal   (Followers: 52)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
Building Simulation     Hybrid Journal   (Followers: 2)
Bulletin of Statistics     Full-text available via subscription   (Followers: 4)
CHANCE     Hybrid Journal   (Followers: 5)
Communications in Statistics - Simulation and Computation     Hybrid Journal   (Followers: 9)
Communications in Statistics - Theory and Methods     Hybrid Journal   (Followers: 11)
Computational Statistics     Hybrid Journal   (Followers: 14)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 37)
Current Research in Biostatistics     Open Access   (Followers: 8)
Decisions in Economics and Finance     Hybrid Journal   (Followers: 11)
Demographic Research     Open Access   (Followers: 15)
Electronic Journal of Statistics     Open Access   (Followers: 8)
Engineering With Computers     Hybrid Journal   (Followers: 5)
Environmental and Ecological Statistics     Hybrid Journal   (Followers: 7)
ESAIM: Probability and Statistics     Full-text available via subscription   (Followers: 5)
Extremes     Hybrid Journal   (Followers: 2)
Fuzzy Optimization and Decision Making     Hybrid Journal   (Followers: 9)
Geneva Papers on Risk and Insurance - Issues and Practice     Hybrid Journal   (Followers: 13)
Handbook of Numerical Analysis     Full-text available via subscription   (Followers: 5)
Handbook of Statistics     Full-text available via subscription   (Followers: 7)
IEA World Energy Statistics and Balances -     Full-text available via subscription   (Followers: 2)
International Journal of Computational Economics and Econometrics     Hybrid Journal   (Followers: 6)
International Journal of Quality, Statistics, and Reliability     Open Access   (Followers: 17)
International Journal of Stochastic Analysis     Open Access   (Followers: 3)
International Statistical Review     Hybrid Journal   (Followers: 13)
International Trade by Commodity Statistics - Statistiques du commerce international par produit     Full-text available via subscription  
Journal of Algebraic Combinatorics     Hybrid Journal   (Followers: 4)
Journal of Applied Statistics     Hybrid Journal   (Followers: 21)
Journal of Biopharmaceutical Statistics     Hybrid Journal   (Followers: 21)
Journal of Business & Economic Statistics     Full-text available via subscription   (Followers: 39, SJR: 3.664, CiteScore: 2)
Journal of Combinatorial Optimization     Hybrid Journal   (Followers: 7)
Journal of Computational & Graphical Statistics     Full-text available via subscription   (Followers: 20)
Journal of Econometrics     Hybrid Journal   (Followers: 84)
Journal of Educational and Behavioral Statistics     Hybrid Journal   (Followers: 6)
Journal of Forecasting     Hybrid Journal   (Followers: 17)
Journal of Global Optimization     Hybrid Journal   (Followers: 7)
Journal of Interactive Marketing     Hybrid Journal   (Followers: 10)
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Nonparametric Statistics     Hybrid Journal   (Followers: 6)
Journal of Probability and Statistics     Open Access   (Followers: 10)
Journal of Risk and Uncertainty     Hybrid Journal   (Followers: 33)
Journal of Statistical and Econometric Methods     Open Access   (Followers: 5)
Journal of Statistical Physics     Hybrid Journal   (Followers: 13)
Journal of Statistical Planning and Inference     Hybrid Journal   (Followers: 8)
Journal of Statistical Software     Open Access   (Followers: 21, SJR: 13.802, CiteScore: 16)
Journal of the American Statistical Association     Full-text available via subscription   (Followers: 72, SJR: 3.746, CiteScore: 2)
Journal of the Korean Statistical Society     Hybrid Journal   (Followers: 1)
Journal of the Royal Statistical Society Series C (Applied Statistics)     Hybrid Journal   (Followers: 33)
Journal of the Royal Statistical Society, Series A (Statistics in Society)     Hybrid Journal   (Followers: 27)
Journal of the Royal Statistical Society, Series B (Statistical Methodology)     Hybrid Journal   (Followers: 43)
Journal of Theoretical Probability     Hybrid Journal   (Followers: 3)
Journal of Time Series Analysis     Hybrid Journal   (Followers: 16)
Journal of Urbanism: International Research on Placemaking and Urban Sustainability     Hybrid Journal   (Followers: 30)
Law, Probability and Risk     Hybrid Journal   (Followers: 8)
Lifetime Data Analysis     Hybrid Journal   (Followers: 7)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Measurement Interdisciplinary Research and Perspectives     Hybrid Journal   (Followers: 1)
Metrika     Hybrid Journal   (Followers: 4)
Modelling of Mechanical Systems     Full-text available via subscription   (Followers: 1)
Monte Carlo Methods and Applications     Hybrid Journal   (Followers: 6)
Monthly Statistics of International Trade - Statistiques mensuelles du commerce international     Full-text available via subscription   (Followers: 2)
Multivariate Behavioral Research     Hybrid Journal   (Followers: 5)
Optimization Letters     Hybrid Journal   (Followers: 2)
Optimization Methods and Software     Hybrid Journal   (Followers: 8)
Oxford Bulletin of Economics and Statistics     Hybrid Journal   (Followers: 34)
Pharmaceutical Statistics     Hybrid Journal   (Followers: 17)
Probability Surveys     Open Access   (Followers: 4)
Queueing Systems     Hybrid Journal   (Followers: 7)
Research Synthesis Methods     Hybrid Journal   (Followers: 8)
Review of Economics and Statistics     Hybrid Journal   (Followers: 128)
Review of Socionetwork Strategies     Hybrid Journal  
Risk Management     Hybrid Journal   (Followers: 15)
Sankhya A     Hybrid Journal   (Followers: 2)
Scandinavian Journal of Statistics     Hybrid Journal   (Followers: 9)
Sequential Analysis: Design Methods and Applications     Hybrid Journal  
Significance     Hybrid Journal   (Followers: 7)
Sociological Methods & Research     Hybrid Journal   (Followers: 38)
SourceOCDE Comptes nationaux et Statistiques retrospectives     Full-text available via subscription  
SourceOCDE Statistiques : Sources et methodes     Full-text available via subscription  
SourceOECD Bank Profitability Statistics - SourceOCDE Rentabilite des banques     Full-text available via subscription   (Followers: 1)
SourceOECD Insurance Statistics - SourceOCDE Statistiques d'assurance     Full-text available via subscription   (Followers: 2)
SourceOECD Main Economic Indicators - SourceOCDE Principaux indicateurs economiques     Full-text available via subscription   (Followers: 1)
SourceOECD Measuring Globalisation Statistics - SourceOCDE Mesurer la mondialisation - Base de donnees statistiques     Full-text available via subscription  
SourceOECD Monthly Statistics of International Trade     Full-text available via subscription   (Followers: 1)
SourceOECD National Accounts & Historical Statistics     Full-text available via subscription  
SourceOECD OECD Economic Outlook Database - SourceOCDE Statistiques des Perspectives economiques de l'OCDE     Full-text available via subscription   (Followers: 2)
SourceOECD Science and Technology Statistics - SourceOCDE Base de donnees des sciences et de la technologie     Full-text available via subscription  
SourceOECD Statistics Sources & Methods     Full-text available via subscription   (Followers: 1)
SourceOECD Taxing Wages Statistics - SourceOCDE Statistiques des impots sur les salaires     Full-text available via subscription  
Stata Journal     Full-text available via subscription   (Followers: 9)
Statistica Neerlandica     Hybrid Journal   (Followers: 1)
Statistical Applications in Genetics and Molecular Biology     Hybrid Journal   (Followers: 5)
Statistical Communications in Infectious Diseases     Hybrid Journal  
Statistical Inference for Stochastic Processes     Hybrid Journal   (Followers: 3)
Statistical Methodology     Hybrid Journal   (Followers: 7)
Statistical Methods and Applications     Hybrid Journal   (Followers: 6)
Statistical Methods in Medical Research     Hybrid Journal   (Followers: 27)
Statistical Modelling     Hybrid Journal   (Followers: 19)
Statistical Papers     Hybrid Journal   (Followers: 4)
Statistical Science     Full-text available via subscription   (Followers: 13)
Statistics & Probability Letters     Hybrid Journal   (Followers: 13)
Statistics & Risk Modeling     Hybrid Journal   (Followers: 3)
Statistics and Computing     Hybrid Journal   (Followers: 13)
Statistics and Economics     Open Access   (Followers: 1)
Statistics in Medicine     Hybrid Journal   (Followers: 197)
Statistics, Politics and Policy     Hybrid Journal   (Followers: 6)
Statistics: A Journal of Theoretical and Applied Statistics     Hybrid Journal   (Followers: 14)
Stochastic Models     Hybrid Journal   (Followers: 3)
Stochastics An International Journal of Probability and Stochastic Processes: formerly Stochastics and Stochastics Reports     Hybrid Journal   (Followers: 2)
Structural and Multidisciplinary Optimization     Hybrid Journal   (Followers: 12)
Teaching Statistics     Hybrid Journal   (Followers: 7)
Technology Innovations in Statistics Education (TISE)     Open Access   (Followers: 2)
TEST     Hybrid Journal   (Followers: 3)
The American Statistician     Full-text available via subscription   (Followers: 23)
The Annals of Applied Probability     Full-text available via subscription   (Followers: 8)
The Annals of Probability     Full-text available via subscription   (Followers: 10)
The Annals of Statistics     Full-text available via subscription   (Followers: 34)
The Canadian Journal of Statistics / La Revue Canadienne de Statistique     Hybrid Journal   (Followers: 11)
Wiley Interdisciplinary Reviews - Computational Statistics     Hybrid Journal   (Followers: 1)

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Similar Journals
Journal Cover
Journal of Statistical Physics
Journal Prestige (SJR): 0.93
Citation Impact (citeScore): 1
Number of Followers: 13  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9613 - ISSN (Online) 0022-4715
Published by Springer-Verlag Homepage  [2652 journals]
  • Interface Roughening in Two Dimensions
    • Abstract: Roughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of \(w^2\) is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of \(w^2\) , which differs from results in the literature. It is confirmed by Monte Carlo simulations.
      PubDate: 2021-03-12
       
  • Limit Theorems and Fluctuations for Point Vortices of Generalized Euler
           Equations
    • Abstract: We prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean-field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.
      PubDate: 2021-03-12
       
  • Brownian Motion at the Speed of Light: A New Lorentz Invariant Family of
           Processes
    • Abstract: We consider here a new family of processes which describe particles which only can move at the speed of light c in the ordinary 3D physical space. The velocity, which randomly changes direction, can be represented as a point on the surface of a sphere of radius c and its trajectories only may connect points of this variety. A process can be constructed both by considering jumps from one point to another (velocity changes discontinuously) and by continuous velocity trajectories on the surface. We recently proposed to follow this second strategy assuming that the velocity is described by a Wiener process (which is isotropic only in the ’rest frame’) on the surface of the sphere. Using both Ito calculus and Lorentz boost rules, we succeed here in characterizing the entire Lorentz-invariant family of processes. Moreover, we highlight and describe the short-term ballistic behavior versus the long-term diffusive behavior of the particles in the 3D physical space.
      PubDate: 2021-03-11
       
  • Fluctuations of Linear Statistics for Gaussian Perturbations of the
           Lattice $${\mathbb {Z}}^d$$ Z d
    • Abstract: We study the point process W in \({\mathbb {R}}^d\) obtained by adding an independent Gaussian vector to each point in \({\mathbb {Z}}^d\) . Our main concern is the asymptotic size of fluctuations of the linear statistics in the large volume limit, defined as $$\begin{aligned} N(h,R) = \sum _{w\in W} h\left( \frac{w}{R}\right) , \end{aligned}$$ where \(h\in \left( L^1\cap L^2\right) ({\mathbb {R}}^d)\) is a test function and \(R\rightarrow \infty \) . We will also consider the stationary counter-part of the process W, obtained by adding to all perturbations a random vector which is uniformly distributed on \([0,1]^d\) and is independent of all the Gaussians. We focus on two main examples of interest, when the test function h is either smooth or is an indicator function of a convex set with a smooth boundary whose curvature does not vanish.
      PubDate: 2021-03-07
       
  • Efficient Numerical Evaluation of Thermodynamic Quantities on Infinite
           (Semi-)classical Chains
    • Abstract: This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical discretization of integral kernels using quadrature rules. For analytic kernels, the technique exhibits exponential convergence in the number of quadrature points. As demonstration, we apply the method to a classical particle chain, to the semiclassical nonlinear Schrödinger (NLS) equation and to a classical system on a cylindrical lattice. A comparison with molecular dynamics simulations performed for the NLS model shows very good agreement.
      PubDate: 2021-03-06
       
  • The Free Energy of a Quantum Sherrington–Kirkpatrick Spin-Glass
           Model for Weak Disorder
    • Abstract: We extend two rigorous results of Aizenman, Lebowitz, and Ruelle in their pioneering paper of 1987 on the Sherrington–Kirkpatrick spin-glass model without external magnetic field to the quantum case with a “transverse field” of strength \(\mathsf {b}\) . More precisely, if the Gaussian disorder is weak in the sense that its standard deviation \(\mathsf {v}>0\) is smaller than the temperature \(1/\beta \) , then the (random) free energy almost surely equals the annealed free energy in the macroscopic limit and there is no spin-glass phase for any \(\mathsf {b}/\mathsf {v}\ge 0\) . The macroscopic annealed free energy turns out to be non-trivial and given, for any \(\beta \mathsf {v}>0\) , by the global minimum of a certain functional of square-integrable functions on the unit square according to a Varadhan large-deviation principle. For \(\beta \mathsf {v}<1\) we determine this minimum up to the order \((\beta \mathsf {v})^{4}\) with the Taylor coefficients explicitly given as functions of \(\beta \mathsf {b}\) and with a remainder not exceeding \((\beta \mathsf {v})^{6}/16\) . As a by-product we prove that the so-called static approximation to the minimization problem yields the wrong \(\beta \mathsf {b}\) -dependence even to lowest order. Our main tool for dealing with the non-commutativity of the spin-operator components is a probabilistic representation of the Boltzmann–Gibbs operator by a Feynman–Kac (path-integral) formula based on an independent collection of Poisson processes in the positive half-line with common rate \(\beta \mathsf {b}\) . Its essence dates back to Kac in 1956, but the formula was published only in 1989 by Gaveau and Schulman.
      PubDate: 2021-03-06
       
  • Boundary CFT and Tensor Network Approach to Surface Critical Phenomena of
           the Tricritical 3-State Potts model
    • Abstract: One-dimensional edges of classical systems in two dimension sometimes show surprisingly rich phase transitions and critical phenomena, particularly when the bulk is at criticality. As such a model, we study the surface critical behavior of the 3-state dilute Potts model whose bulk is tuned at the tricritical point. To investigate it more precisely than in the previous works (Deng and Blöte, Phys Rev E 70:035107, 2004; Phys Rev E 71:026109, 2005), we analyze it from the viewpoint of the boundary conformal field theory (BCFT). The complete classification of the conformal boundary conditions for the minimal BCFTs discussed in Behrend et al. (Nucl Phys B 579:707, 2000) allows us to collect the twelve boundary fixed points in the tricritical 3-state Potts BCFT. Employing the tensor network renormalization method, we numerically study the surface phase diagram of the tricritical 3-state Potts model in detail, and reveal that the eleven boundary fixed points among the twelve can be realized on the lattice by controlling the external field and coupling strength at the boundary. The last unfound fixed point would be out of the physically sound region in the parameter space, similarly to the ‘new’ boundary condition in the 3-state Potts BCFT.
      PubDate: 2021-03-06
       
  • Flooding dynamics of diffusive dispersion in a random potential
    • Abstract: We discuss the combined effects of overdamped motion in a quenched random potential and diffusion, in one dimension, in the limit where the diffusion coefficient is small. Our analysis considers the statistics of the mean first-passage time T(x) to reach position x, arising from different realisations of the random potential. Specifically, we contrast the median \({\bar{T}}(x)\) , which is an informative description of the typical course of the motion, with the expectation value \(\langle T(x)\rangle \) , which is dominated by rare events where there is an exceptionally high barrier to diffusion. We show that at relatively short times the median \({\bar{T}}(x)\) is explained by a ‘flooding’ model, where T(x) is predominantly determined by the highest barriers which are encountered before reaching position x. These highest barriers are quantified using methods of extreme value statistics.
      PubDate: 2021-03-05
       
  • On the Statistical Stability of Families of Attracting Sets and the
           Contracting Lorenz Attractor
    • Abstract: We present criteria for statistical stability of attracting sets for vector fields using dynamical conditions on the corresponding generated flows. These conditions are easily verified for all singular-hyperbolic attracting sets of \(C^2\) vector fields using known results, providing robust examples of statistically stable singular attracting sets (encompassing in particular the Lorenz and geometrical Lorenz attractors). These conditions are shown to hold also on the persistent but non-robust family of contracting Lorenz flows (also known as Rovella attractors), providing examples of statistical stability among members of non-open families of dynamical systems. In both instances, our conditions avoid the use of detailed information about perturbations of the one-dimensional induced dynamics on specially chosen Poincaré sections.
      PubDate: 2021-03-03
       
  • Some Remarks on Replicated Simulated Annealing
    • Abstract: Recently authors have introduced the idea of training discrete weights neural networks using a mix between classical simulated annealing and a replica ansatz known from the statistical physics literature. Among other points, they claim their method is able to find robust configurations. In this paper, we analyze this so called “replicated simulated annealing” algorithm. In particular, we give criteria to guarantee its convergence, and study when it successfully samples from configurations. We also perform experiments using synthetic and real data bases.
      PubDate: 2021-03-02
       
  • Infinite Level GREM-Like K-Processes Existence and Convergence
    • Abstract: We derive the existence of infinite level GREM-like K-processes by taking the limit of a sequence of finite level versions of such processes as the number of levels diverges. The main step in the derivation is obtaining the convergence of the sequence of underlying finite level clock processes. This is accomplished by perturbing these processes so as to turn them into martingales, and resorting to martingale convergence to obtain convergence for the perturbed clock processes; nontriviality of the limit requires a specific choice of parameters of the original process; we conclude the step by showing that the perturbation washes away in the limit. The perturbation is done by inserting suitable factors into the expression of the clocks, as well as rescaling the resulting expression suitably; the existence of such factors is itself established through martingale convergence.
      PubDate: 2021-03-02
       
  • Uniform Threshold for Fixation of the Stochastic Sandpile Model on the
           Line
    • Abstract: We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate 1, sending two of its particles to neighbouring sites chosen independently. We show that when the initial average density is less than 1/2, the system locally fixates almost surely. We achieve this bound by analysing the parity of the total number of times each site is visited by a large number of particles under the sandpile dynamics.
      PubDate: 2021-03-02
       
  • Statistical Mechanical Foundation of Weber–Fechner Laws
    • Abstract: Weber–Fechner laws are phenomenological relations describing a logarithmic relation between perception and sensory stimulus in a great variety of organisms. While firmly established, a theoretical argument for those laws in terms of relevant models or from statistical physics is largely missing. We present such a discussion in terms of response theory for nonequilibrium systems, where the induced displacement or current, which stands for the perceived stimulus, crucially depends on the change in time-symmetric reactivities. Stationary nonequilibria may indeed generate extra currents by changing the dynamical activity. The argument finishes by understanding how the extra dynamical activity logarithmically encodes the actual stimulus.
      PubDate: 2021-03-01
       
  • Moderate Deviations for the SSEP with a Slow Bond
    • Abstract: We consider the one dimensional symmetric simple exclusion process with a slow bond. In this model, particles cross each bond at rate \(N^2\) , except one particular bond, the slow bond, where the rate is N. Above, N is the scaling parameter. This model has been considered in the context of hydrodynamic limits, fluctuations and large deviations. We investigate moderate deviations from hydrodynamics and obtain a moderate deviation principle.
      PubDate: 2021-02-26
       
  • Stochastic Limit-Cycle Oscillations of a Nonlinear System Under Random
           Perturbations
    • Abstract: Dynamical systems with \(\varepsilon \) small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a time-inhomogeneous Gaussian process, near a deterministic limit cycle in \(\mathbb {R}^n\) . Based on respectively the theory of random perturbations of dynamical systems and the WKB approximation that codes the large deviations principle (LDP), results are developed in parallel from both standpoints of stochastic trajectories and transition probability density and their relations are elucidated. We show rigorously the correspondence between the local Gaussian fluctuations and the curvature of the large deviation rate function near its infimum, connecting the CLT and the LDP of diffusion processes. We study uniform asymptotic behavior of stochastic limit cycles through the interchange of limits of time \(t\rightarrow \infty \) and \(\varepsilon \rightarrow 0\) . Three further characterizations of stochastic limit cycle oscillators are obtained: (i) An approximation of the probability flux near the cycle; (ii) Two special features of the vector field for the cyclic motion; (iii) A local entropy balance equation along the cycle with clear physical meanings. Lastly and different from the standard treatment, the origin of the \(\varepsilon \) in the theory is justified by a novel scaling hypothesis via constructing a sequence of stochastic differential equations.
      PubDate: 2021-02-25
       
  • Bivectorial Nonequilibrium Thermodynamics: Cycle Affinity, Vorticity
           Potential, and Onsager’s Principle
    • Abstract: We generalize an idea in the works of Landauer and Bennett on computations, and Hill’s in chemical kinetics, to emphasize the importance of kinetic cycles in mesoscopic nonequilibrium thermodynamics (NET). For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affinity \(\nabla \wedge \big (\mathbf{D}^{-1}\mathbf{b}\big )\) and vorticity potential \(\mathbf{A}(\mathbf{x})\) of the stationary flux \(\mathbf{J}^{*}=\nabla \times \mathbf{A}\) . Each bivectorial cycle couples two transport processes represented by vectors and gives rise to Onsager’s notion of reciprocality; the scalar product of the two bivectors \(\mathbf{A}\cdot \nabla \wedge \big (\mathbf{D}^{-1}\mathbf{b}\big )\) is the rate of local entropy production in the nonequilibrium steady state. An Onsager operator that relates vorticity to cycle affinity is introduced.
      PubDate: 2021-02-24
       
  • Diffusion Approximation for Noise-Induced Evolution of First Integrals in
           Multifrequency Systems
    • Abstract: We consider fast oscillating random perturbations of dynamical systems in regions where one can introduce action-angle-type coordinates. In an appropriate time scale, the evolution of first integrals, under the assumption that the set of resonance tori is small enough, is approximated by a diffusion process. If action-angle coordinates can be introduced only piece-wise, the limiting diffusion process should be considered on an open-book space. Such a process can be described by differential operators, one in each page, supplemented by some gluing conditions at the binding of the open book.
      PubDate: 2021-02-23
       
  • On Entropy Production of Repeated Quantum Measurements II. Examples
    • Abstract: We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various interesting phenomena and singularities. We emphasize the role of the thermodynamic formalism, and give many examples of quantum instruments whose resulting probability measures on the space of infinite sequences of outcomes (shift space) do not have the (weak) Gibbs property. We also discuss physically relevant examples where the entropy production rate satisfies a large deviation principle but fails to obey the central limit theorem and the fluctuation–dissipation theorem. Throughout the analysis, we explore the connections with other, a priori unrelated topics like functions of Markov chains, hidden Markov models, matrix products and number theory.
      PubDate: 2021-02-22
       
  • Integrability and Braided Tensor Categories
    • Abstract: Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on the Boltzmann weights admitting a conserved current, generalising one found using quantum-group algebras. The resulting trigonometric weights are typically those of a critical integrable lattice model, so the method here gives a linear way of “Baxterising”, i.e. building a solution of the Yang-Baxter equation out of topological data. It also illuminates why many models do not admit a solution. I discuss many examples in geometric and local models, including (perhaps) a new solution.
      PubDate: 2021-02-18
       
  • A Local Barycentric Version of the Bak–Sneppen Model
    • Abstract: We study the behaviour of an interacting particle system, related to the Bak–Sneppen model and Jante’s law process defined in Kennerberg and Volkov (Adv Appl Probab 50:414–439, 2018). Let \(N\ge 3\) vertices be placed on a circle, such that each vertex has exactly two neighbours. To each vertex assign a real number, called fitness (we use this term, as it is quite standard for Bak–Sneppen models). Now find the vertex which fitness deviates most from the average of the fitnesses of its two immediate neighbours (in case of a tie, draw uniformly among such vertices), and replace it by a random value drawn independently according to some distribution \(\zeta \) . We show that in case where \(\zeta \) is a finitely supported or continuous uniform distribution, all the fitnesses except one converge to the same value.
      PubDate: 2021-02-15
       
 
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