01/06/2022, 17:00 — 18:00 — Online
Cristina Toninelli, University Paris Dauphine - PSL
Fredrickson-Andersen 2-spin facilitated model: sharp threshold
The Fredrickson-Andersen 2-spin facilitated model (FA-2f) on $Z^d$ is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring cooperative and glassy dynamics. For FA-2f vacancies facilitate motion: a particle can be created/killed on a site only if at least $2$ of its nearest neighbors are empty. We will present sharp results for the first time, $\tau$, at which the origin is emptied for the stationary process when the density of empty sites ($q$) is small: in any dimension $d \geq 2$ it holds $\tau \sim \exp \left( \tfrac{ d \lambda(d,2) +o(1)} {q^{1/(d-1)}} \right)$ w.h.p., with $\lambda (d,2)$ the threshold constant for the 2-neighbour bootstrap percolation on $Z^d$. This is the first sharp result for a critical KCM and settles various controversies accumulated in physics literature over the last four decades. Joint work with I. Hartarsky and F. Martinelli
