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  Subjects -> MATHEMATICS (Total: 1040 journals)
    - APPLIED MATHEMATICS (83 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (770 journals)
    - MATHEMATICS (GENERAL) (43 journals)
    - NUMERICAL ANALYSIS (23 journals)
    - PROBABILITIES AND MATH STATISTICS (98 journals)

MATHEMATICS (770 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: 4)
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     Hybrid Journal   (Followers: 38)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 9)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 21)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 17)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 17)
Advances in Mathematical Physics     Open Access   (Followers: 7)
Advances in Mathematics     Full-text available via subscription   (Followers: 15)
Advances in Nonlinear Analysis     Open Access  
Advances in Numerical Analysis     Open Access   (Followers: 7)
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: 8)
Advances in Pure Mathematics     Open Access   (Followers: 9)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 2)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
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: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 3)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 13)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 7)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
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: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 25)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
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)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
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: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 13)
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: 3)
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: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
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)
Chaos, Solitons & Fractals : X     Open Access  
ChemSusChem     Hybrid Journal   (Followers: 8)
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: 3)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 15)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 4)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
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: 10)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
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: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
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: 4)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal  
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: 2)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Combinatorics, Probability and Computing
Journal Prestige (SJR): 0.839
Citation Impact (citeScore): 1
Number of Followers: 4  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0963-5483 - ISSN (Online) 1469-2163
Published by Cambridge University Press Homepage  [387 journals]
  • Positive association of the oriented percolation cluster in randomly
           oriented graphs
    • Authors: François Bienvenu
      Pages: 811 - 815
      Abstract: Consider any fixed graph whose edges have been randomly and independently oriented, and write {S ⇝} to indicate that there is an oriented path going from a vertex s ∊ S to vertex i. Narayanan (2016) proved that for any set S and any two vertices i and j, {S ⇝ i} and {S ⇝ j} are positively correlated. His proof relies on the Ahlswede–Daykin inequality, a rather advanced tool of probabilistic combinatorics.In this short note I give an elementary proof of the following, stronger result: writing V for the vertex set of the graph, for any source set S, the events {S ⇝ i}, i ∊ V, are positively associated, meaning that the expectation of the product of increasing functionals of the family {S ⇝ i} for i ∊ V is greater than the product of their expectations.
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S0963548319000191
      Issue No: Vol. 28, No. 6 (2019)
       
  • A natural barrier in random greedy hypergraph matching
    • Authors: Patrick Bennett; Tom Bohman
      Pages: 816 - 825
      Abstract: Let r ⩾ 2 be a fixed constant and let $ {\cal H} $ be an r-uniform, D-regular hypergraph on N vertices. Assume further that D → ∞ as N → ∞ and that degrees of pairs of vertices in $ {\cal H} $ are at most L where L = D/( log N)ω(1). We consider the random greedy algorithm for forming a matching in $ {\cal H} $ . We choose a matching at random by iteratively choosing edges uniformly at random to be in the matching and deleting all edges that share at least one vertex with a chosen edge before moving on to the next choice. This process terminates when there are no edges remaining in the graph. We show that with high probability the proportion of vertices of $ {\cal H} $ that are not saturated by the final matching is at most (L/D)(1/(2(r−1)))+o(1). This point is a natural barrier in the analysis of the random greedy hypergraph matching process.
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S0963548319000051
      Issue No: Vol. 28, No. 6 (2019)
       
  • On the union of intersecting families
    • Authors: David Ellis; Noam Lifshitz
      Pages: 826 - 839
      Abstract: A family of sets is said to be intersecting if any two sets in the family have non-empty intersection. In 1973, Erdős raised the problem of determining the maximum possible size of a union of r different intersecting families of k-element subsets of an n-element set, for each triple of integers (n, k, r). We make progress on this problem, proving that for any fixed integer r ⩾ 2 and for any $$k \le ({1 \over 2} - o(1))n$$ , if X is an n-element set, and $${\cal F} = {\cal F}_1 \cup {\cal F}_2 \cup \cdots \cup {\cal F}_r $$ , where each $$ {\cal F}_i $$ is an intersecting family of k-element subsets of X, then $$|{\cal F}| \le \left( {\matrix{n \cr k \cr } } \right) - \left( {\matrix{{n - r} \cr k \cr } } \right)$$ , with equality only if $${\cal F} = \{ S \subset X:|S| = k,\;S \cap R \ne \emptyset \} $$ for some R ⊂ X with |R| = r. This is best possible up to the size of the o(1) term, and improves a 1987 result of Frankl and Füredi, who obtained the same conclusion under the stronger hypothesis $$k < (3 - \sqrt 5 )n/2$$ , in the case r = 2. Our proof utilizes an isoperimetric, influence-based method recently developed by Keller and the authors.
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S096354831900004X
      Issue No: Vol. 28, No. 6 (2019)
       
  • k-Partite+k-Graphs+and+Loose+Cycles&rft.title=Combinatorics,+Probability+and+Computing&rft.issn=0963-5483&rft.date=2019&rft.volume=28&rft.spage=840&rft.epage=870&rft.aulast=Gao&rft.aufirst=Wei&rft.au=Wei+Gao&rft.au=Jie+Han,+Yi+Zhao&rft_id=info:doi/10.1017/S096354831900021X">Codegree Conditions for Tiling Complete k-Partite k-Graphs and Loose
           Cycles
    • Authors: Wei Gao; Jie Han, Yi Zhao
      Pages: 840 - 870
      Abstract: Given two k-graphs (k-uniform hypergraphs) F and H, a perfect F-tiling (or F-factor) in H is a set of vertex-disjoint copies of F that together cover the vertex set of H. For all complete k-partite k-graphs K, Mycroft proved a minimum codegree condition that guarantees a K-factor in an n-vertex k-graph, which is tight up to an error term o(n). In this paper we improve the error term in Mycroft’s result to a sublinear term that relates to the Turán number of K when the differences of the sizes of the vertex classes of K are co-prime. Furthermore, we find a construction which shows that our improved codegree condition is asymptotically tight in infinitely many cases, thus disproving a conjecture of Mycroft. Finally, we determine exact minimum codegree conditions for tiling K(k)(1, … , 1, 2) and tiling loose cycles, thus generalizing the results of Czygrinow, DeBiasio and Nagle, and of Czygrinow, respectively.
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S096354831900021X
      Issue No: Vol. 28, No. 6 (2019)
       
  • On the Size-Ramsey Number of Cycles
    • Authors: R. Javadi; F. Khoeini, G. R. Omidi, A. Pokrovskiy
      Pages: 871 - 880
      Abstract: For given graphs G1,…, Gk, the size-Ramsey number $\hat R({G_1}, \ldots ,{G_k})$ is the smallest integer m for which there exists a graph H on m edges such that in every k-edge colouring of H with colours 1,…,k, H contains a monochromatic copy of Gi of colour i for some 1 ≤ i ≤ k. We denote $\hat R({G_1}, \ldots ,{G_k})$ by ${\hat R_k}(G)$ when G1 = ⋯ = Gk = G.Haxell, Kohayakawa and Łuczak showed that the size-Ramsey number of a cycle Cn is linear in n, ${\hat R_k}({C_n}) \le {c_k}n$ for some constant ck. Their proof, however, is based on Szemerédi’s regularity lemma so no specific constant ck is known.In this paper, we give various upper bounds for the size-Ramsey numbers of cycles. We provide an alternative proof of ${\hat R_k}({C_n}) \le {c_k}n$ , avoiding use of the regularity lemma, where ck is exponential and doubly exponential in k, when n is even and odd, respectively. In particular, we show that for sufficiently large n we have ${\hat R_2}({C_n}) \le {10^5} \times cn$ , where c = 6.5 if n is even and c = 1989 otherwise.
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S0963548319000221
      Issue No: Vol. 28, No. 6 (2019)
       
  • On Erdős–Ko–Rado for random hypergraphs I
    • Authors: A. Hamm; J. Kahn
      Pages: 881 - 916
      Abstract: A family of sets is intersecting if no two of its members are disjoint, and has the Erdős–Ko–Rado property (or is EKR) if each of its largest intersecting subfamilies has non-empty intersection.Denote by ${{\cal H}_k}(n,p)$ the random family in which each k-subset of {1, …, n} is present with probability p, independent of other choices. A question first studied by Balogh, Bohman and Mubayi asks: \begin{equation} {\rm{For what }}p = p(n,k){\rm{is}}{{\cal H}_k}(n,p){\rm{likely to be EKR}}? \end{equation} Here, for fixed c < 1/4, and $k \lt \sqrt {cn\log n} $ we give a precise answer to this question, characterizing those sequences p = p(n, k) for which \begin{equation} {\mathbb{P}}({{\cal H}_k}(n,p){\rm{is EKR}}{\kern 1pt} ) \to 1{\rm{as }}n \to \infty . \end{equation}
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S0963548319000117
      Issue No: Vol. 28, No. 6 (2019)
       
  • Erratum to ‘On Percolation and the Bunkbed Conjecture’
    • Authors: Svante Linusson
      Pages: 917 - 918
      Abstract: There was an incorrect argument in the proof of the main theorem in ‘On percolation and the bunkbed conjecture’, in Combin. Probab. Comput. (2011) 20 103–117 doi: 10.1017/S0963548309990666. I thus no longer claim to have a proof for the bunkbed conjecture for outerplanar graphs.
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S0963548319000038
      Issue No: Vol. 28, No. 6 (2019)
       
  • Logarithmic Sobolev inequalities in discrete product spaces
    • Authors: Katalin Marton
      Pages: 919 - 935
      Abstract: The aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: for a fixed probability measure q on , ( is a finite set), and any probability measure on ,(*) $$D(p||q){\rm{\le}}C \cdot \sum\limits_{i = 1}^n {{\rm{\mathbb{E}}}_p D(p_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,...,{\rm{ }}Y_n )||q_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,{\rm{ }}...,{\rm{ }}Y_n )),} $$ where pi(· |y1, …, yi−1, yi+1, …, yn) and qi(· |x1, …, xi−1, xi+1, …, xn) denote the local specifications for p resp. q, that is, the conditional distributions of the ith coordinate, given the other coordinates. The constant C depends on (the local specifications of) q.The inequality (*) ismeaningful in product spaces, in both the discrete and the continuous case, and can be used to prove a logarithmic Sobolev inequality for q, provided uniform logarithmic Sobolev inequalities are available for qi(· |x1, …, xi−1, xi+1, …, xn), for all fixed i and fixed (x1, …, xi−1, xi+1, …, xn). Inequality (*) directly implies that the Gibbs sampler associated with q is a contraction for relative entropy.In this paper we derive inequality (*), and thereby a logarithmic Sobolev inequality, in discrete product spaces, by proving inequalities for an appropriate Wasserstein-like distance.
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S0963548319000099
      Issue No: Vol. 28, No. 6 (2019)
       
  • An Improved Upper Bound for Bootstrap Percolation in All Dimensions
    • Authors: Andrew J. Uzzell
      Pages: 936 - 960
      Abstract: In r-neighbour bootstrap percolation on the vertex set of a graph G, a set A of initially infected vertices spreads by infecting, at each time step, all uninfected vertices with at least r previously infected neighbours. When the elements of A are chosen independently with some probability p, it is natural to study the critical probability pc(G, r) at which it becomes likely that all of V(G) will eventually become infected. Improving a result of Balogh, Bollobás and Morris, we give a bound on the second term in the expansion of the critical probability when G = [n]d and d ⩾ r ⩾ 2. We show that for all d ⩾ r ⩾ 2 there exists a constant cd,r > 0 such that if n is sufficiently large, then $$p_c (\left[ n \right]^d ,{\rm{ }}r){\rm{\le }}\left( {\frac{{\lambda (d,r)}}{{\log _{(r - 1)} (n)}} - \frac{{c_{d,r} }}{{(\log _{(r - 1)} (n))^{3/2} }}} \right)^{d - r + 1} ,$$ where λ(d, r) is an exact constant and log(k) (n) denotes the k-times iterated natural logarithm of n.
      PubDate: 2019-11-01T00:00:00.000Z
      DOI: 10.1017/S0963548319000130
      Issue No: Vol. 28, No. 6 (2019)
       
 
 
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