{
  "id": "2203.01102",
  "version": "v1",
  "published": "2022-03-02T13:41:46.000Z",
  "updated": "2022-03-02T13:41:46.000Z",
  "title": "Maximum and records of random walks with stochastic resetting",
  "authors": [
    "Claude Godrèche",
    "Jean-Marc Luck"
  ],
  "comment": "35 pages, 6 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We revisit the statistics of extremes and records of symmetric random walks with stochastic resetting, extending earlier studies in several directions. We put forward a diffusive scaling regime (symmetric step length distribution with finite variance, weak resetting probability) where the maximum of the walk and the number of its records up to discrete time $n$ become asymptotically proportional to each other for single typical trajectories. Their distributions obey scaling laws ruled by a common two-parameter scaling function, interpolating between a half-Gaussian and a Gumbel law. The exact solution of the problem for the symmetric exponential step length distribution and for the simple Polya lattice walk, as well as a heuristic analysis of other distributions, allow a quantitative study of several facets of the statistics of extremes and records beyond the diffusive scaling regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-02T13:41:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walks",
      "stochastic resetting",
      "symmetric exponential step length distribution",
      "obey scaling laws",
      "symmetric step length distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}