4 problems

Let $G$ be a finite graph of maximum degree $\Delta$, let $P$ be the Glauber transition matrix at complex fugacity $w$, and let $\operatorname{spr}(P)$ denote its spectral radius o…

Let $G$ be a finite claw-free graph, meaning that it has no induced subgraph isomorphic to $K_{1,3}$. Let $Z(w)$ be the hard-core lattice-gas partition function of $G$. Hamidoune–S…

Let $G$ be a countably infinite graph of maximum degree … , the hard-core lattice gas on $G$ has a unique Gibbs measure whenever … for all vertices $x$; perhaps this remains true w…

Soft-core transition-time conjecture. There exists a time $t_{NG}(\beta)$ such that the time-evolved measure is Gibbs for all $t<t_{NG}(\beta)$ and non-Gibbs for all…