APPROXIMATING STATIONARY DISTRIBUTIONS OF FAST MIXING GLAUBER DYNAMICS, WITH APPLICATIONS TO EXPONENTIAL RANDOM GRAPHS

• 成果类型: Article
• 署名作者: Reinert, Gesine; Ross, Nathan
• 署名单位: University of Oxford; University of Melbourne
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1478
• 发表日期: 2019
• 页码: 3201-3229
• 关键词: local limit-theorems; random-variables; steins method; convergent sequences; sums

摘要

We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple expectation of the other. The result is applied to estimate, with explicit error, expectations of functions of random vectors for some Ising models and exponential random graphs in high temperature regimes.