Condensation transition in the late-time position of a run-and-tumble particle – Archive ouverte HAL

Francesco Mori ¹ Pierre Le Doussal ² Satya N. Majumdar ¹ Grégory Schehr ³ Pierre Le Doussal ² Satya Majumdar ¹

Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr, Pierre Le Doussal, et al.. Condensation transition in the late-time position of a run-and-tumble particle. Physical Review E , American Physical Society (APS), 2021, 103 (6), ⟨10.1103/PhysRevE.103.062134⟩. ⟨hal-03301446⟩

We study the position distribution $P(\vec{R},N)$ of a run-and-tumble particle (RTP) in arbitrary dimension $d$, after $N$ runs. We assume that the constant speed $v>0$ of the particle during each running phase is independently drawn from a probability distribution $W(v)$ and that the direction of the particle is chosen isotropically after each tumbling. The position distribution is clearly isotropic, $P(\vec{R},N)\to P(R,N)$ where $R=|\vec{R}|$. We show that, under certain conditions on $d$ and $W(v)$ and for large $N$, a condensation transition occurs at some critical value of $R=R_c\sim O(N)$ located in the large deviation regime of $P(R,N)$. For $R

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