{
  "id": "1901.02742",
  "version": "v1",
  "published": "2019-01-09T13:44:06.000Z",
  "updated": "2019-01-09T13:44:06.000Z",
  "title": "Explicit speed of convergence of the stochastic billiard in a convex set",
  "authors": [
    "Ninon Fétique"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we are interested in the speed of convergence of the stochastic billiard evolving in a convex set K. This process can be described as follows: a particle moves at unit speed inside the set K until it hits the boundary, and is randomly reflected, independently of its position and previous velocity. We focus on convex sets in R 2 with a curvature bounded from above and below. We give an explicit coupling for both the continuous-time process and the embedded Markov chain of hitting points on the boundary, which leads to an explicit speed of convergence to equilibrium.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-09T13:44:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex set",
      "convergence",
      "particle moves",
      "unit speed inside",
      "continuous-time process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}