{
  "id": "1004.2398",
  "version": "v1",
  "published": "2010-04-14T14:02:38.000Z",
  "updated": "2010-04-14T14:02:38.000Z",
  "title": "Mirror coupling of reflecting Brownian motion and an application to Chavel's conjecture",
  "authors": [
    "Mihai N. Pascu"
  ],
  "comment": "21 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In a series of papers, Burdzy et. al. introduced the \\emph{mirror coupling} of reflecting Brownian motions in a smooth bounded domain $D\\subset \\mathbb{R}^{d}$, and used it to prove certain properties of eigenvalues and eigenfunctions of the Neumann Laplaceian on $D$. In the present paper we show that the construction of the mirror coupling can be extended to the case when the two Brownian motions live in different domains $D_{1},D_{2}\\subset \\mathbb{R}^{d}$. As an application of the construction, we derive a unifying proof of the two main results concerning the validity of Chavel's conjecture on the domain monotonicity of the Neumann heat kernel, due to I. Chavel (\\cite{Chavel}), respectively W. S. Kendall (\\cite{Kendall}).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-14T14:02:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60H20",
      "35K05"
    ],
    "keywords": [
      "reflecting brownian motion",
      "chavels conjecture",
      "mirror coupling",
      "application",
      "neumann heat kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.2398P"
    }
  }
}