{
  "id": "2205.00817",
  "version": "v1",
  "published": "2022-05-02T11:44:10.000Z",
  "updated": "2022-05-02T11:44:10.000Z",
  "title": "Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity",
  "authors": [
    "Eric Bertin"
  ],
  "comment": "12 pages, submitted to special issue of J. Phys. A on \"Stochastic Resetting: Theory and Applications\"",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs only beyond a threshold distance from the origin. This problem is motivated by physical realizations like soft matter under shear, where diffusion of a walk is induced by resetting events of other walks. We first reformulate in the broader context of diffusion with stochastic resetting the so-called H\\'ebraud-Lequeux model for plasticity in dense soft matter, in which diffusivity is proportional to the average resetting rate. Depending on parameter values, the response to a weak external field may be either linear or non-linear with a non-zero average position for a vanishing applied field, and the transition between these two regimes may be interpreted as a continuous phase transition. Extending the model by considering a general power-law relation between diffusivity and average resetting rate, we notably find a discontinuous phase transition between a finite diffusivity and a vanishing diffusivity in the small field limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-02T11:44:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic resetting",
      "random walks",
      "resetting-rate-dependent diffusivity",
      "average resetting rate",
      "population"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}