2 problems

Let $\mathcal{G}$ be an infinite, irreducible, bounded-degree graph, let $\nu_{L,o}$ denote the $L$-step heat-kernel measure rooted at $o$, and let $\partial A$ be the boundary of…

Slow-thermalization conjecture. Starting from the uniform measure, Langevin dynamics takes exponential time to reach equilibrium for every $T<T_{sh}$: there is a constant $c>0$ suc…