The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher

Abstract

We consider the heat equation with a multiplicative Gaussian potential in dimensions $d\ge 3$. We show that the renormalized solution converges to the solution of a deterministic diffusion equation with an effective diffusivity. We also prove that the renormalized large scale random fluctuations are described by the Edwards-Wilkinson model, that is, the stochastic heat equation (SHE) with additive white noise, with an effective variance.

33 pages, minor revisions

References in corpus (1)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions

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