The theory of fluctuating hydrodynamics aims to describe density fluctuations of interacting particle systems as so-called Dean–Kawasaki stochastic partial differential equations. However, Dean–Kawasaki equations are ill-posed and the focus has shifted towards finding well-posed approximations that retain the statistical properties of the particle system. In this talk, we consider the fluctuating hydrodynamics of a system in which particles are attracted to one another through a Coulomb force (Keller–Segel dynamics). We propose an additive-noise approximation and show that it retains the same law of large numbers and central limit theorem as (conjectured for) the particle system. We further deduce a large deviation principle and show that the approximation error lies in the skeleton equation that drives the rate function. Based on joint work with Avi Mayorcas.

**Date**: 26 February 2024, 14:00 (Monday, 7th week, Hilary 2024)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Speaker**: Adrian Martini (University of Oxford)**Organising department**: Department of Statistics**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Members of the University only- Editors: James Martin, Julien Berestycki