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

2024/05/02 by Sotirios Kotitsas, Kotitsas, Sotirios · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2405.01519

openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the stochastic PDE: ∂_tu(t,x)=(1)/(2)Δu(t,x)+βu(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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