STATIONARY DISTRIBUTIONS FOR THE VOTER MODEL IN d ≥ 3 ARE FACTORS OF IID

• 成果类型: Article
• 署名作者: Sly, Allan; Zhang, Lingfu
• 署名单位: Princeton University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1568
• 发表日期: 2022
• 页码: 1589-1609
• 关键词: finitary codings; entropy

摘要

For the Voter Model on Z(d), d >= 3, we show that the (extremal) stationary distributions are isomorphic to Bernoulli shifts, and answer an open question asked by Steif and Tykesson in (ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 899-955). The proof gives explicit constructions of the stationary distributions as factors of IID processes on Z(d).