{
  "id": "math/0206281",
  "version": "v1",
  "published": "2002-06-26T17:26:13.000Z",
  "updated": "2002-06-26T17:26:13.000Z",
  "title": "Large time behavior of the heat kernel",
  "authors": [
    "Yehuda Pinchover"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "In this paper we study the large time behavior of the (minimal) heat kernel $k_P^M(x,y,t)$ of a general time independent parabolic operator $L=u_t+P(x, \\partial_x)$ which is defined on a noncompact manifold $M$. More precisely, we prove that $$\\lim_{t\\to\\infty} e^{\\lambda_0 t}k_P^{M}(x,y,t)$$ always exists. Here $\\lambda_0$ is the generalized principal eigenvalue of the operator $P$ in $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-06-26T17:26:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "60J60",
      "35B40",
      "58J35"
    ],
    "keywords": [
      "large time behavior",
      "heat kernel",
      "general time independent parabolic operator",
      "noncompact manifold",
      "generalized principal eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......6281P"
    }
  }
}