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Hidde van Wiechen

Publications and source records attributed to Hidde van Wiechen.

4 recordsLinked to original sources
arXiv2025

Hydrodynamic limit and large deviations for run-and-tumble particles with mean-field switching rates

In this paper, we study run-and-tumble particles moving on two copies of the discrete torus (referred to as layers), where the switching rate between layers depends on a mean-field interaction among the particles. We derive the hydrodynamic limit of this model, as well as the large deviations from the hydrodynamic limit. Our main tool is the introduction of a weakly perturbed version of the system, whose hydrodynamic equations precisely characterize the trajectories associated with large deviations.

math.PR↗
arXiv2024

A large deviation principle for the multispecies stirring process

In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the method of the foundational paper [1] based on the superexponential estimate to the multispecies setting. This requires a careful choice of the corresponding weakly asymmetric dynamics, which is parametrized by fields depending on the various species. We also prove the hydrodynamic limit of this weakly asymmetric dynamics, which is similar to but different from the ABC model in [2]. Using the appropriate asymmetric dynamics, we also obtain that the mobility matrix relating the drift currents to the fields coincides with the covariance matrix of the reversible multinomial distribution, which then further leads to the Einstein relation

math.PR↗
arXiv2024

Stationary fluctuations of run-and-tumble particles

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.

math.PR↗