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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2018

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

Résumé

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.

Dates et versions

hal-01794966 , version 1 (18-05-2018)

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Kanaya Malakar, V. Jemseena, Anupam Kundu, K. Vijay Kumar, Sanjib Sabhapandit, et al.. Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension. Journal of Statistical Mechanics: Theory and Experiment, 2018, pp.043215. ⟨10.1088/1742-5468/aab84f⟩. ⟨hal-01794966⟩
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