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.

引用

页码：2002 / 2027

页数：26

共 35 条

[1] Rapid mixing for lattice colourings with fewer colours
Achlioptas, D
Molloy, M
Moore, C
Van Bussel, F
[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2005, : 217 - 228
[2] FOLNER INDEPENDENCE AND THE AMENABLE ISING-MODEL
ADAMS, S
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1992, 12 : 633 - 657
[3] Boyle M, 2008, CONTEMP MATH, V469, P69
[4] Chandgotia N, 2021, COMMUN MATH PHYS, V387, P621, DOI 10.1007/s00220-021-04181-0
[5] ENTROPY OF ABELIAN GROUP OF TRANSFORMATIONS
CONZE, JP
[J]. ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1972, 25 (01): : 11 - 30
[6] den Hollander F, 1997, J ANAL MATH, V72, P165
[7] On K-automorphisms, Bernoulli shifts and Markov random fields
DenHollander, F
Steif, JE
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1997, 17 : 405 - 415
[8] Duminil-Copin, 2022, PREPRINT
[9] Duminil-Copin H., 2017, PIMS CRM SUMMER SCH, P161
[10] Long-range order in the 3-state antiferromagnetic Potts model in high dimensions
Feldheim, Ohad N.
Spinka, Yinon
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2019, 21 (05) : 1509 - 1570

← 1 2 3 4 →