Edwards-Wilkinson limit for a stochastic advection-diffusion PDE

Sotirios Kotitsas; Dejun Luo; Mario Maurelli

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arXiv · 2509.07956

Edwards-Wilkinson limit for a stochastic advection-diffusion PDE

Sotirios Kotitsas·Dejun Luo·Mario Maurelli

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Abstract

We consider a diffusion in a Gaussian random environment that is white in time and study the large-scale behavior of the quenched density with respect to the Lebesgue measure. We show that under diffusive rescaling, the fluctuations of the density converge to a Gaussian limit, described by an additive stochastic heat equation. In the case where the environment is divergence-free, our result can be interpreted as computing the scaling limit of the first-order correction to the quenched Central Limit Theorem.

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Sotirios Kotitsas, Dejun Luo, Mario Maurelli. 2025-09-09. Edwards-Wilkinson limit for a stochastic advection-diffusion PDE. https://arxiv.org/abs/2509.07956

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