{
  "id": "2004.00177",
  "version": "v1",
  "published": "2020-04-01T00:35:49.000Z",
  "updated": "2020-04-01T00:35:49.000Z",
  "title": "Large-scale behavior of a particle system with mean-field interaction: Traveling wave solutions",
  "authors": [
    "Alexander Stolyar"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real line. Specifically, each particle \"jumps forward\" at some time points, with the instantaneous rate of jumps given by a decreasing function of the particle's location quantile within the overall distribution of particle locations. A mean-field model describes the evolution of the particles' distribution, when $n$ is large. It is essentially a solution to an integro-differential equation within a certain class. Our main results concern the existence and uniqueness of -- and attraction to -- mean-field models which are traveling waves, under general conditions on the jump-rate function and the jump-size distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-01T00:35:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90B15",
      "60K25"
    ],
    "keywords": [
      "particle system",
      "traveling wave solutions",
      "mean-field interaction",
      "large-scale behavior",
      "mean-field model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}