Stationary Fluctuations of Run-and-Tumble Particles

Journal article (2024)

Authors

Research Group

Applied Probability () (TU Delft)

Memory effects Ornstein-Uhlenbeck process Path large deviations Run-and-tumble motion Stationary fluctuations Stochastic duality

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Published Date

2024

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

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 also consider 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, and obtain its covariance in closed form. By considering small noise limits of this non-Markovian Gaussian process, we obtain in a concrete example a large deviation rate function containing memory terms.