Proper 3-colorings of $\mathbb{Z}^2$ are Bernoulli

Gourab Ray; Yinon Spinka

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arXiv · 2004.00028

Proper 3-colorings of $\mathbb{Z}^2$ are Bernoulli

Gourab Ray·Yinon Spinka

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Abstract

We consider the unique measure of maximal entropy for proper 3-colorings of $\mathbb{Z}^2$, 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 $\mathbb{Z}^2$. Along the way, we obtain various estimates on the mixing properties of this measure.

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Gourab Ray, Yinon Spinka. 2020-03-31. Proper 3-colorings of $\mathbb{Z}^2$ are Bernoulli. https://arxiv.org/abs/2004.00028

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