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The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher (1710.00344v2)
Published 1 Oct 2017 in math.PR, math-ph, math.AP, and math.MP
Abstract: We consider the heat equation with a multiplicative Gaussian potential in dimensions $d\geq 3$. 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.