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Diffusivity of random walks in random environments

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I will survey recent results on diffusive bounds and central limit theorem for some models of RWRE . Full CLT is established for random walks in divergence-free random drift field, under the $H_{-1}$ condition, in any dimension. Diffusive bounds are established for RWRE under the assumption of existence of absolutely continuous invariant distribution of the environment seen from the random walker, in three and more dimensions. The content of the talk is based on joint work with Gady Kozma, respectively Christophe Sabot (in progress).

This talk is part of the Probability series.

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