Speaker:

Fabio Martinelli

Title:

Glauber dynamics for constrained spin models on trees.

Abstract:

We analyze kinetically constrained 0-1 spin models (KCSM) on rooted and unrooted trees of finite connectivity. These tree models are particularly relevant in physics literature since some of them undergo an ergodicity breaking transition with the mixed first-second order character of the glass transition. Here we first identify the ergodicity regime and prove that the critical density coincide with that of a suitable bootstrap percolation model. Next we prove positivity of the spectral gap in the whole ergodic regime via a novel argument based on martingales ideas. Finally we show a polynomial (in the depth of the tree) bound on the mixing time at the critical. point. We will also discuss an interesting open problem.