Martedi' 17 dicembre 2013 alle ore 16 presso l'aula 1BC50
del Dipartimento di Matematica di Padova
il Prof. Fabio Martinelli (Dip. di Matematica, Universita' di Roma Tre)
terra' il seguente seminario
Title: Time scales separation and dynamical heterogeneities in
the East model.
Abstract:
The East model is a finite linear Markov chain of 0-1 spins, evolving
according to a very simple rule:
i) with rate 1 and independently for each vertex, a new value 1/0 is
proposed with probability 1-q and q respectively;
ii) the proposed value is accepted iff the spin immediately to the left is
0.
The model and its generalizations play an important role as models of the
dynamics of real glasses.
The parameter q, which turns out to be the density of the zeros (the
facilitating spins) in the stationary measure,
is assumed to be very small. In the physical literature this setting
corresponds to a low temperature case.
We will examine the problem of dynamic heterogeneity, i.e. non-trivial
spatio-temporal fluctuations of the local relaxation to equilibrium.
A key result will be a very precise computation of the relaxation time of
the chain as a function of q and of its length,
which uses induction on length scales on one hand and a novel algorithmic
lower bound on the other.
Our findings reject non rigorous approaches based on numerical simulations.
We will conclude with a conjecture due to D. Aldous and P. Diaconis about
the scaling limit of the East chain as q-->0.
Joint work with A. Faggionato and P. Chleboun