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The Gaussian free field as a stream function: asymptotics of effective diffusivity in infra-red cut-off

  • Lihan Wang (MPI MiS, Leipzig)
E1 05 (Leibniz-Saal)

Abstract

We investigate the effective diffusivity of a random drift-diffusion operator that is at the borderline of standard stochastic homogenization theory: In two space-dimensions, we consider the divergence-free drift with stream function given by the Gaussian free-field, with an ultra-violet cut-off at scale unity and an infra-red cut-off at a scale L. We establish the precise scaling of how the effective diffusivity diverges in terms of L, specifying recent results based on a Wiener chaos decomposition and a mathematical physics-type analysis in the corresponding Fock space. This amounts to the study of convection-enhanced diffusion at the borderline to anomalous diffusion. It provides a quantitative stochastic homogenization perspective, and therefore yields quenched rather than annealed results. Joint work with Georgiana Chatzigeorgiou, Peter Morfe and Felix Otto (MPI).

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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