MIXING TIMES FOR A CONSTRAINED ISING PROCESS ON THE TORUS AT LOW DENSITY

• 成果类型: Article
• 署名作者: Pillai, Natesh S.; Smith, Aaron
• 署名单位: Harvard University; University of Ottawa
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1080
• 发表日期: 2017
• 页码: 1003-1070
• 关键词: coalescing random-walks; glass-transition; northeast model; markov-chains; voter model; bounds

摘要

We study a kinetically constrained Ising process (KCIP) associated with a graph G and density parameter p; this process is an interacting particle system with state space {0, 1}(G), the location of the particles. The number of particles at stationarity follows the Binomial(vertical bar G vertical bar, p) distribution, conditioned on having at least one particle. The constraint in the name of the process refers to the rule that a vertex cannot change its state unless it has at least one neighbour in state 1. The KCIP has been proposed by statistical physicists as a model for the glass transition, and more recently as a simple algorithm for data storage in computer networks. In this note, we study the mixing time of this process on the torusG = Z(L)(d), d >= 3, in the low-density regime p = c/vertical bar G vertical bar for arbitrary 0 < c