# Pierre Nyquist: Continuum limit for a finite-size particle system: Large deviations and gradient flows

**Time: **
Tue 2020-02-11 15.15 - 16.15

**Lecturer: **
Pierre Nyquist, KTH

**Location: **
KTH, F11

### Abstract

Many stochastic particle systems have well-defined continuum limits: as the number of particles tends to infinity, the density of particles converges to a deterministic limit that satisfies a partial differential equation. In this talk I will discuss a specific example of this: a system consisting of particles with finite size. In two and three dimensions they are spheres, in one dimension rods. The particles move by Brownian noise and cannot overlap with each other, leading to a strong interaction with neighbouring particles. Previous studies include numerical simulations and formal asymptotic results, along with conjectures on the limit, but no rigorous results.

In the talk we will consider the one-dimensional setting and a scaling in which the number of particles tend to infinity while the volume fraction of the rods remain constant. Using large deviations for empirical measures we give a complete picture of the convergence of the particle system and derive the gradient flow structure for the limit evolution. The latter gives clear interpretations for the driving functional and the dissipation metric and how they derive from the underlying particle system.

This is based on joint work with Nir Gavish and Mark Peletier.