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Title
An Additive-Noise Approximation to Keller–Segel–Dean–Kawasaki Dynamics
Abstract
The theory of fluctuating hydrodynamics aims to describe density fluctuations of interacting particle systems as so-called Dean–Kawasaki stochastic partial differential equations. However, those Dean–Kawasaki equations are ill-posed and recent 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.
Please note that the seminar will take place in person in room 130 of Huxley Building.