{
  "id": "1907.03632",
  "version": "v1",
  "published": "2019-07-08T14:11:01.000Z",
  "updated": "2019-07-08T14:11:01.000Z",
  "title": "Survival probability of stochastic processes beyond persistence exponents",
  "authors": [
    "N. Levernier",
    "M. Dolgushev",
    "O. Bénichou",
    "R. Voituriez",
    "T. Guérin"
  ],
  "journal": "Nature Communications 2019",
  "doi": "10.1038/s41467-019-10841-6",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "For many stochastic processes, the probability $S(t)$ of not-having reached a target in unbounded space up to time $t$ follows a slow algebraic decay at long times, $S(t)\\sim S_0/t^\\theta$. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent $\\theta$ has been studied at length, the prefactor $S_0$, which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for $S_0$ for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for $S_0$ are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-08T14:11:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic processes",
      "persistence exponent",
      "survival probability",
      "unbounded space",
      "fractional brownian motion"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Nature"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}