文章基本信息

标题：Random-Cluster Dynamics in Z^2: Rapid Mixing with General Boundary Conditions
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作者：Antonio Blanca ; Reza Gheissari ; Eric Vigoda 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：145
页码：1-19
DOI：10.4230/LIPIcs.APPROX-RANDOM.2019.67
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The random-cluster (FK) model is a key tool for the study of phase transitions and for the design of efficient Markov chain Monte Carlo (MCMC) sampling algorithms for the Ising/Potts model. It is well-known that in the high-temperature region beta1 and p != p_c(q) the mixing time of the FK-dynamics is polynomial in n for every realizable boundary condition. Previously, for boundary conditions that do not carry long-range information (namely wired and free), Blanca and Sinclair (2017) had proved that the FK-dynamics in the same setting mixes in optimal O(n^2 log n) time. To illustrate the difficulties introduced by general boundary conditions, we also construct a class of non-realizable boundary conditions that induce slow (stretched-exponential) convergence at high temperatures.
关键词：Markov chain; mixing time; random-cluster model; Glauber dynamics; spatial mixing