{
  "id": "2211.16173",
  "version": "v1",
  "published": "2022-11-29T13:05:29.000Z",
  "updated": "2022-11-29T13:05:29.000Z",
  "title": "Effects of mortality on stochastic search processes with resetting",
  "authors": [
    "Mattia Radice"
  ],
  "comment": "13 pages, 4 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the first-passage time to the origin of a mortal Brownian particle, with mortality rate $\\mu$, diffusing in one dimension. The particle starts its motion from $x>0$ and it is subject to stochastic resetting with constant rate $r$. We first show that the probability of reaching the target is closely related to the mean first-passage time of the corresponding problem in absence of mortality. We then consider the mean and the variance of the first-passage time conditioned on the event that the particle reaches the target before dying. When the average lifetime $\\tau_\\mu=1/\\mu$ satisfies $\\tau_\\mu>\\alpha\\tau_D$, where $\\tau_D=x^2/(4D)$ is the diffusive time scale and $\\alpha\\approx1.575$ is a constant, there is a resetting rate $r_\\mu^*$ that maximizes the probability, and there may also be a different rate $r_m$ that minimizes the average time of a successful search; on the other hand, for average lifetimes $\\tau_\\mu<\\beta\\tau_D$, with $\\beta\\approx0.2884$, resetting progressively eliminates slower search processes, resulting in decreasing mean first-passage times but also decreasing the probability of success. Intermediate regimes are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-29T13:05:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic search processes",
      "mean first-passage time",
      "average lifetime",
      "progressively eliminates slower search processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}