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 50 条

[1] Random sampling of 3-colorings in Z2
Goldberg, LA
Martin, R
Paterson, M
RANDOM STRUCTURES & ALGORITHMS, 2004, 24 (03) : 279 - 302
[2] (Z2)3-COLORINGS AND RIGHT-ANGLED HYPERBOLIC 3-MANIFOLDS
Li, Youlin
Ma, Jiming
PACIFIC JOURNAL OF MATHEMATICS, 2013, 263 (02) : 419 - 434
[3] On Proper Edge 3-Colorings of a Cubic Graph
Karpov D.V.
Journal of Mathematical Sciences, 2021, 255 (1) : 17 - 27
[4] Symmetric colorings of G X Z2
Phakathi, Jabulani
Zelenyuk, Yevhen
Zelenyuk, Yuliya
ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS, 2023, 11 (02) : 381 - 387
[5] FORBIDDEN SUBGRAPHS AND 3-COLORINGS
Fan, Genghua
Xu, Baogang
Ye, Tianjun
Yu, Xingxing
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2014, 28 (03) : 1226 - 1256
[6] On 3-colorings of plane graphs
Xu B.-G.
Acta Mathematicae Applicatae Sinica, 2004, 20 (4) : 597 - 604
[7] ON 3-COLORINGS OF E(KN)
KIM, JH
DISCRETE MATHEMATICS, 1993, 118 (1-3) : 269 - 273
[8] Counting symmetric colorings of G x Z2
Phakathi, Jabulani
Singh, Shivani
Zelenyuk, Yevhen
Zelenyuk, Yuliya
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2019, 18 (10)
[9] Finding Paths Between 3-Colorings
Cereceda, Luis
van den Heuvel, Jan
Johnson, Matthew
JOURNAL OF GRAPH THEORY, 2011, 67 (01) : 69 - 82
[10] Rigidity of 3-colorings of the discrete torus
Feldheim, Ohad Noy
Peled, Ron
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2018, 54 (02): : 952 - 994

← 1 2 3 4 5 →