FINITELY DEPENDENT PROCESSES ARE FINITARY

• 成果类型: Article
• 署名作者: Spinka, Yinon
• 署名单位: University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1417
• 发表日期: 2020
• 页码: 2088-2117
• 关键词: invariant percolation

摘要

We show that any finitely dependent invariant process on a transitive amenable graph is a finitary factor of an i.i.d. process. With an additional assumption on the geometry of the graph, namely that no two balls with different centers are identical, we further show that the i.i.d. process may be taken to have entropy arbitrarily close to that of the finitely dependent process. As an application, we give an affirmative answer to a question of Holroyd (Ann. Inst. Henri Poincare Probab. Stat. 53 (2017) 753-765).