Occupation time of a run-and-tumble particle with resetting

Abstract

We study the positive occupation time of a run-and-tumble particle (RTP) subject to stochastic resetting. Under the resetting protocol, the position of the particle is reset to the origin at a random sequence of times that is generated by a Poisson process with rate $r$. The velocity state is reset to $\pm v$ with fixed probabilities ${\rho }_1$ and ${\rho }_{-1}=1-{\rho }_1$, where $v$ is the speed. We exploit the fact that the moment generating functions with and without resetting are related by a renewal equation, and the latter generating function can be calculated by solving a corresponding Feynman-Kac equation. This allows us to numerically locate in Laplace space the largest real pole of the moment generating function with resetting, and thus derive a large deviation principle (LDP) for the occupation time probability density using the Gartner-Ellis theorem. We explore how the LDP depends on the switching rate $\alpha$ of the velocity state, the resetting rate $r$ and the probability ${\rho }_1$. In particular, we show that the corresponding LDP for a Brownian particle with resetting is recovered in the fast switching limit $\alpha \to \infty$. On the other hand, the behavior in the slow switching limit depends on ${\rho }_1$ in the resetting protocol.

arXiv comment13 pages, 6 figures

References in corpus (23)

• Active Particles in Complex and Crowded Environments
• The large deviation approach to statistical mechanics
• Motility-Induced Phase Separation
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• Run and tumble particle under resetting: a renewal approach
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties
• Large deviations for Markov processes with resetting
• Work fluctuations and Jarzynski equality in stochastic resetting
• First-passage time of run-and-tumble particles
• Symmetric Exclusion Process under Stochastic Resetting
• A First-Order Dynamical Transition in the displacement distribution of a Driven Run-and-Tumble Particle
• On the area under a continuous time Brownian motion till its first-passage time
• Stationary superstatistics distributions of trapped run-and-tumble particles
• Active processes in one dimension
• Properties of additive functionals of Brownian motion with resetting
• Generalised `Arcsine' laws for run-and-tumble particle in one dimension
• Non-crossing run-and-tumble particles on a line
• Local time of diffusion with stochastic resetting
• Ramifications of disorder on active particles in one dimension

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