- Séminaire / Formations,
Séminaire MODAL'X : Cristina Toninelli (CEREMADE, CNRS et Université Paris Dauphine)
Publié le 8 novembre 2022
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Mis à jour le 2 janvier 2023
Fredrickson-Andersen 2-spin facilitated model: sharp threshold
Date(s)
le 5 janvier 2023
13h30-14h30
Lieu(x)
Abstract : The Fredrickson-Andersen 2-spin facilitated model (FA-2f) on Zd is a paradig- matic 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, τ, at which the origin is emptied for the stationary process when the density of empty sites (q) is small: in any dimension d ≥ 2 it holds
τ ∼ exp [ (dλ(d,2)+o(1)) / q^{1/(d−1)}]
w.h.p., with λ(d, 2) the threshold constant for the 2-neighbour bootstrap percolation on Zd. This is the first sharp result for a critical KCM and settles various controversies accumulated in physics literature over the last four decades.
We will explain the dominant relaxation mechanism leading to this result, give a flavour of the proof techniques, and discuss further results that can be obtained via our technique for more general KCM, including full universality results in two dimensions.
[Joint work with I.Hartarsky and F.Martinelli]
τ ∼ exp [ (dλ(d,2)+o(1)) / q^{1/(d−1)}]
w.h.p., with λ(d, 2) the threshold constant for the 2-neighbour bootstrap percolation on Zd. This is the first sharp result for a critical KCM and settles various controversies accumulated in physics literature over the last four decades.
We will explain the dominant relaxation mechanism leading to this result, give a flavour of the proof techniques, and discuss further results that can be obtained via our technique for more general KCM, including full universality results in two dimensions.
[Joint work with I.Hartarsky and F.Martinelli]
Mis à jour le 02 janvier 2023