Stationary fluctuations of run-and-tumble particles
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916156144615424 |
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| author | Redig, Frank van Wiechen, Hidde |
| author_facet | Redig, Frank van Wiechen, Hidde |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02967 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stationary fluctuations of run-and-tumble particles Redig, Frank van Wiechen, Hidde Probability Mathematical Physics 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. |
| title | Stationary fluctuations of run-and-tumble particles |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2307.02967 |