MALLOWS PERMUTATIONS AND FINITE DEPENDENCE

• 成果类型: Article
• 署名作者: Holroyd, Alexander E.; Hutchcroft, Tom; Levy, Avi
• 署名单位: University of Washington; University of Washington Seattle; University of Cambridge; Microsoft
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1363
• 发表日期: 2020
• 页码: 343-379
• 关键词: representations

摘要

We use the Mallows permutation model to construct a new family of stationary finitely dependent proper colorings of the integers. We prove that these colorings can be expressed as finitary factors of i.i.d. processes with finite mean coding radii. They are the first colorings known to have these properties. Moreover, we prove that the coding radii have exponential tails, and that the colorings can also be expressed as functions of countable-state Markov chains. We deduce analogous existence statements concerning shifts of finite type and higher-dimensional colorings.