Proper 3-colorings of Z2 are Bernoulli

被引：4
|
作者：
Ray, Gourab [1 ]
Spinka, Yinon [2 ,3 ]
机构：
[1] Univ Victoria, Dept Math, Victoria, BC V8W 2Y2, Canada
[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
[3] Tel Aviv Univ, Sch Math Sci, IL-6997801 Tel Aviv, Israel
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2023年 / 43卷 / 06期
基金：
加拿大自然科学与工程研究理事会;
关键词：
coloring; Bernoulli; factor of iid; FINITARY CODINGS; AUTOMORPHISMS; INDEPENDENCE; MODEL;
D O I：
10.1017/etds.2021.160
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the unique measure of maximal entropy for proper 3-colorings of Z(2) , or equivalently, the so-called zero-slope Gibbs measure. Our main result is that this measure is Bernoulli, or equivalently, that it can be expressed as the image of a translation-equivariant function of independent and identically distributed random variables placed on Z(2). Along the way, we obtain various estimates on the mixing properties of this measure.
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页码：2002 / 2027
页数：26
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