A central limit theorem for nonlinear conservative SPDEs

Andrea Clini; Benjamin Fehrman

A central limit theorem for nonlinear conservative SPDEs

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arxiv 2310.19924 v1 pith:ZQFNTPHN submitted 2023-10-30 math.PR math.AP

Andrea Clini , Benjamin Fehrman This is my paper · ORCID

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We prove a central limit theorem characterizing the small noise fluctuations of stochastic PDEs of fluctuating hydrodynamics type. The results apply to the case of nonlinear and potentially degenerate diffusions and irregular noise coefficients including the square root. In several cases, the fluctuations of the solutions agree to first order with the fluctuations of certain interacting particle systems about their hydrodynamic limits.

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Stochastic PDE approach to fluctuating interfaces
math.PR 2024-12 conditional novelty 7.0 of 10

For a flat immobile interface in a particle system, the interface fluctuation converges, after suitable scaling, to Brownian motion in d=1 and to the stochastic heat equation in d>=2.

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