AbstractIn this talk we consider the stochastic homogenization of elliptic non-divergence form equations on the integer lattice and the corresponding model of random walks in random environment (RWRE) which is a martingale. We will derive the optimal rates of the homogenization for the Dirichlet problem. We will also discuss the correlation structure of the invariant measure and quantitative es...
Abstract：We consider the Facilitated Exclusion Process (FEP) in one dimension, which is an interacting particle system with degenerate rates. In this model, a particle could jump if and only if there is one particle in its neighbors and no particle at the target site. We derive stationary fluctuations for the FEP in the symmetric, weakly asymmetric and asymmetric cases. In particular, we obser...
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