3 problems

Stability conjecture. For any detailed balance dynamics in the uniqueness regime, uniqueness is stable under small non-detailed-balance perturbations.

Let ${\mathbb Z}^d$ be the nearest-neighbor graph on the $d$-dimensional integer lattice. For an integer $q\geq 3$, consider the $q$-coloring model, whose Gibbs measures are infini…

Let ${\mathbb Z}^d$ be the nearest-neighbor graph on the $d$-dimensional integer lattice, and let a Gibbs measure be an infinite-volume measure obtained as a subsequential limit of…