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.