Equilibrium fluctuations of run-and-tumble particles

Frank Redig, Hidde van Wiechen

Published 2023-07-06Version 1

In this paper we study the stationary fluctuations of independent run-and-tumble particles. We prove that the joint densities of particles with given internal state converges to an infinite dimensional Ornstein Uhlenbeck process. We discuss also an interacting case, where the particles are subjected to exclusion. We then study the fluctuations of the total density, which is a non-Markovian Gaussian process. By considering small noise limits of this process, we obtain in a concrete example a large deviation rate function containing memory terms.