{
  "id": "2006.06989",
  "version": "v1",
  "published": "2020-06-12T08:10:38.000Z",
  "updated": "2020-06-12T08:10:38.000Z",
  "title": "Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension",
  "authors": [
    "Francesco Mori",
    "Pierre Le Doussal",
    "Satya N. Majumdar",
    "Gregory Schehr"
  ],
  "comment": "34 pages, 18 figures. This is an extended version of arXiv:2001.01492, published in Physical Review Letters",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider an active run-and-tumble particle (RTP) in $d$ dimensions, starting from the origin and evolving over a time interval $[0,t]$. We examine three different models for the dynamics of the RTP: the standard RTP model with instantaneous tumblings, a variant with instantaneous runs and a general model in which both the tumblings and the runs are non-instantaneous. For each of these models, we use the Sparre Andersen theorem for discrete-time random walks to compute exactly the probability that the $x$ component does not change sign up to time $t$, showing that it does not depend on $d$. As a consequence of this result, we compute exactly other $x$-component properties, namely the distribution of the time of the maximum and the record statistics, showing that they are universal, i.e. they do not depend on $d$. Moreover, we show that these universal results hold also if the speed $v$ of the particle after each tumbling is random, drawn from a generic probability distribution. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 124, 090603 (2020)].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-12T08:10:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "run-and-tumble particle",
      "arbitrary dimension",
      "universal properties",
      "universal results hold",
      "standard rtp model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}