Quenched invariance principle for random walks with time-dependent ergodic degenerate weights

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Date(s) - 22/01/2016
11 h 00 min - 12 h 00 min

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We study a symmetric diffusion in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. We prove a quenched invariance principle and a quenched local central limit theorem for such a diffusion, under some moment conditions on the environment; the key tools are a local maximal inequality and a local parabolic Harnack inequality obtained with Moser’s iteration technique. As a further application of Moser’s iteration scheme, we study a continuous-time random walk on the lattice in an environment of time-dependent random conductances. We assume that the law of the conductances is ergodic with respect to space-time shifts. Also in this case, we prove a quenched invariance principle under some moment conditions on the environment.

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