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Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle

Abstract : We consider an active run-and-tumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$-component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.
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https://hal.archives-ouvertes.fr/hal-02512214
Contributor : Claudine Le Vaou <>
Submitted on : Thursday, March 19, 2020 - 2:37:58 PM
Last modification on : Thursday, April 15, 2021 - 3:08:13 PM

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Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle. Physical Review Letters, American Physical Society, 2020, 124 (9), ⟨10.1103/PhysRevLett.124.090603⟩. ⟨hal-02512214⟩

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