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arXiv · 2405.01519

The heat equation with time-correlated random potential in d=2: Edwards-Wilkinson fluctuations

Sotirios Kotitsas
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Abstract

We consider the stochastic PDE: $\partial_tu(t,x)=\frac{1}{2}\Delta u(t,x)+{\beta}{}u(t,x)V(t,x),$ in dimension $d=2$, where the potential V is the space and time mollification of the two-dimensional space-time white noise. We show that after renormalizing, the fluctuations of the solution converge to the Edwards-Wilkinson limit with an explicit effective variance and constant effective diffusivity. Our main tool is a Markov chain on the space of paths which we use to establish an extension of the Kallianpur-Robbins law to a specific regenerative process.

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Sotirios Kotitsas. 2024-05-02. The heat equation with time-correlated random potential in d=2: Edwards-Wilkinson fluctuations. https://arxiv.org/abs/2405.01519

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