Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367, Fehrman, Benjamin and Gess, Benjamin 2026. Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process. Communications in Mathematical Physics 407 , 74. 10.1007/s00220-026-05587-4

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Abstract

In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs with nonlinear, conservative noise. In the small-noise limit, we show that the fluctuations of the solutions are to first-order the same as the fluctuations of the particle system. Furthermore, the SPDEs correctly simulate the rare events in the particle process. We prove that the solutions satisfy a zero-noise large deviations principle with rate function equal to that describing the deviations of the symmetric simple exclusion process.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Additional Information:	RRS policy applied
Publisher:	Springer
ISSN:	0010-3616
Date of First Compliant Deposit:	17 March 2026
Date of Acceptance:	11 March 2026
Last Modified:	17 Mar 2026 10:30
URI:	https://orca.cardiff.ac.uk/id/eprint/185775

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