Quenched invariance principles for interacting particles systems

par Arianna Giunti (MPI Leipzig)

jeudi 8 déc. 2016, 14:30 → 15:30 Europe/Paris

salle 435 (UMPA)

We consider the stochastic process given by the walk of a tagged particle in the simple symmetric exclusion process and give an optimal upper bound for its transition probability. We discuss this result and motivate how it may be considered as a first building block for the proof of a quenched invariance principle. Our strategy is to take inspiration from the techniques used in the case of random walks in random conductances: In this setting, showing that an invariance principle holds is equivalent to proving homogenization for the random elliptic operator in divergence form which generates the walk. In particular, a quenched invariance principle corresponds to quantitative estimates on the homogenization process in terms of quenched estimates on the sublinearity of the corrector. This talk is based on a joint work with Yu Gu (Stanford University) and Jean-Christophe Mourrat (ENS Lyon).