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arXiv · 1710.00344

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

Yu Gu·Lenya Ryzhik·Ofer Zeitouni
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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.

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Yu Gu, Lenya Ryzhik, Ofer Zeitouni. 2018-05-25. The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher. https://doi.org/10.1007/s00220-018-3202-0

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