3 problems

Let $q \geq 2$ be an integer, let $\beta \in [0,1]$, and consider the $q$-state antiferromagnetic Potts model on graphs of maximum degree $\Delta$. Define … Weak spatial mixing (WS…

Let $T$) be a tree of maximum degree $\Delta$, and let $q$ be the number of colors. The uniform distribution on proper $q$-colorings of $T$ is considered with strong spatial mixing…

Let $\mathbf{M}$ be a branching matrix, and for a specific value $\lambda<\operatorname{WSM}(T_{\mathbf{M}})$ let $V_\lambda$ be the fixed points of the recurrences of the marginal…