We consider the unique measure of maximal entropy for proper 3-colorings of, 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. Along the way, we obtain various estimates on the mixing properties of this measure.
- factor of iid
All Science Journal Classification (ASJC) codes
- Applied Mathematics