Probability Theory and Related Fields

, Volume 125, Issue 3, pp 350–364

Asymptotic of the heat kernel in general Benedicks domains

  • Pierre Collet
  • Servet Martínez
  • Jaime San Martín

DOI: 10.1007/s00440-002-0241-3

Cite this article as:
Collet, P., Martínez, S. & Martín, J. Probab Theory Relat Fields (2003) 125: 350. doi:10.1007/s00440-002-0241-3

Abstract.

 Using a new inequality relating the heat kernel and the probability of survival, we prove asymptotic ratio limit theorems for the heat kernel (and survival probability) in general Benedicks domains. In particular, the dimension of the cone of positive harmonic measures with Dirichlet boundary conditions can be derived from the rate of convergence to zero of the heat kernel (or the survival probability).

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Pierre Collet
    • 1
  • Servet Martínez
    • 2
  • Jaime San Martín
    • 2
  1. 1.C.N.R.S. UMR 7644, Physique Théorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France. e-mail: collet@cpht.polytechnique.frFR
  2. 2.Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, and Centro de Modelamiento Matemático CNRS UMR 2071, Casilla 170-3 Correo 3, Santiago, Chile. e-mail: smartine@dim. uchile.cl;jsanmart@dim.uchile.clCL

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