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This is a Quantitative Study study.

October 19, 2025Open Access

Small noise fluctuations and large deviations of conservative SPDEs with Dirichlet boundary conditions

Key Points

Small noise fluctuations follow a central limit theorem, indicating significant statistical behavior in large systems.
The large deviations principle fits well with the dynamics observed in particle systems like the zero range process.
Our approach enables the analysis of stochastic PDEs on general C^2 domains, addressing both theoretical and practical nuances.
The Dirichlet boundary conditions correspond to actual physical processes such as particle absorption or injection at the boundary.

Abstract

We establish a central limit theorem and large deviations principle that characterises small noise fluctuations of the generalised Dean--Kawasaki stochastic PDE. The fluctuations agree to first order with fluctuations of certain interacting particle systems, such as the zero range process, about their hydrodynamic limits. Our main contribution is that we are able to consider stochastic PDEs on general C² bounded domains with Dirichlet boundary conditions. On the level of particles, the boundary condition corresponds to absorption or injection of particles at the boundary.

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Cite This Study

Shyam Popat (Wed,) studied this question.

synapsesocial.com/papers/68f43f92854d1061a58aca9c https://doi.org/https://doi.org/10.48550/arxiv.2504.17094

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