Proper 3-colorings of ℤ² are Bernoulli

2020/03/31 by Ray, Gourab, Spinka, Yinon
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.00028

Abstract

We consider the unique measure of maximal entropy for proper 3-colorings of ℤ², 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 ℤ². Along the way, we obtain various estimates on the mixing properties of this measure.

Related

• Phase coexistence and torpid mixing in the 3-coloring model on Z^d
• Computing bounds for entropy of stationary Z^d Markov random fields
• Dimension of Gibbs measures with infinite entropy
• Rigidity of proper colorings of ℤ^d
• Three lectures on random proper colorings of ℤ^d