From quenched invariance principle to semigroup convergence with applications to exclusion processes

2023/03/07 by Alberto Chiarini, Chiarini, Alberto, Simone Floreani +3
Mathematics · #Stochastic processes and statistical mechanics #Random Matrices and Applications #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2303.04127

Abstract

Consider a random walk on ℤ^d in a translation-invariant and ergodic random environment and starting from the origin. In this short note, assuming that a quenched invariance principle for the opportunely-rescaled walks holds, we show how to derive an L¹-convergence of the corresponding semigroups. We then apply this result to obtain a quenched pathwise hydrodynamic limit for the simple symmetric exclusion process on ℤ^d, d≥ 2, with i.i.d. symmetric nearest-neighbors conductances ω_xy∈ [0,∞) only satisfying ℚ(ω_xygt;0)gt;p_c , where p_c is the critical value for bond percolation.

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