Stationary Fluctuations of Run-and-Tumble Particles
F. Redig, H. van Wiechen
2024, v.30, Issue 2, 297-331
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.
doi:10.61102/1024-2953-mprf.2024.30.2.003
Keywords: stationary fluctuations, path large deviations, Ornstein-Uhlenbeck process, run-and-tumble motion, memory effects, stochastic duality
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