Mixing time and local exponential ergodicity of the East-like process in \mathbf Z^d

2015/01/09 by Paul Chleboun, Alessandra Faggionato, Chleboun, Paul +3
Mathematics · Physics and Astronomy · #60K35 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1501.02240

openalex publication_date 2015/01/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The East process, a well known reversible linear chain of spins, represents the prototype of a general class of interacting particle systems with constraints modeling the dynamics of real glasses. In this paper we consider a generalization of the East process living in the d-dimensional lattice and we establish new progresses on the out- of-equilibrium behavior. In particular we prove a form of (local) exponential ergodicity when the initial distribution is far from the stationary one and we prove that the mixing time in a finite box grows linearly in the side of the box.

Citations

• Glassy Time-Scale Divergence and Anomalous Coarsening in a Kinetically Constrained Spin Chain

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