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Advanced seminar AG Mathematical Modeling

Monday, 20.01.2025 at 17.00 in B7 - 210

 

Lecture by Adrian Martini (Oxford) on the topic "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.

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