{
  "id": "2105.00880",
  "version": "v1",
  "published": "2021-05-03T14:02:10.000Z",
  "updated": "2021-05-03T14:02:10.000Z",
  "title": "Stochastic processes with competing reinforcements",
  "authors": [
    "Dirk Erhard",
    "Guilherme Reis"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a simple but powerful technique to study processes driven by two or more reinforcement mechanisms in competition. We apply our method to two types of models: to non conservative zero range processes on finite graphs, and to multi-particle random walks with positive and negative reinforcement on the edges. The results hold for a broad class of reinforcement functions, including those with superlinear growth. Our technique consists in a comparison of the original processes with suitable reference models. To implement the comparison we estimate a Radon-Nikodym derivative on a carefully chosen set of trajectories. Our results describe the almost surely long time behaviour of the processes. We also prove a phase transition depending on the strength of the reinforcement functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-03T14:02:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J10",
      "60K35"
    ],
    "keywords": [
      "stochastic processes",
      "competing reinforcements",
      "non conservative zero range processes",
      "reinforcement functions",
      "multi-particle random walks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}