论文标题
$ \ mathbb {z}^2 $的适当的3色为bernoulli
Proper 3-colorings of $\mathbb{Z}^2$ are Bernoulli
论文作者
论文摘要
我们考虑了$ \ mathbb {z}^2 $的适当3色的最大熵的独特度量，或者等效地，所谓的零斜率吉布斯度量。我们的主要结果是，该度量是Bernoulli或等效的，它可以表示为放置在$ \ Mathbb {Z}^2 $上的独立且相同分布的随机变量的翻译等值函数的图像。一路上，我们获得了有关此度量的混合特性的各种估计。
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.
