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Asymptotic of the heat kernel in general Benedicks domains
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  • Published: March 2003

Asymptotic of the heat kernel in general Benedicks domains

  • Pierre Collet1,
  • Servet Martínez2 &
  • Jaime San Martín2 

Probability Theory and Related Fields volume 125, pages 350–364 (2003)Cite this article

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  • 5 Citations

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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).

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Authors and Affiliations

  1. C.N.R.S. UMR 7644, Physique Théorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France. e-mail: collet@cpht.polytechnique.fr, , , , , , FR

    Pierre Collet

  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.cl, , , , , , CL

    Servet Martínez & Jaime San Martín

Authors
  1. Pierre Collet
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  2. Servet Martínez
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  3. Jaime San Martín
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Additional information

Received: 31 March 2002 / Revised version: 12 August 2002 / Published online: 19 December 2002

Mathematics Subject Classification (2000): 60J65, 31B05

Key words or phrases: Positive harmonic functions – Ratio limit theorems – Survival probability

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Collet, P., Martínez, S. & Martín, J. Asymptotic of the heat kernel in general Benedicks domains. Probab Theory Relat Fields 125, 350–364 (2003). https://doi.org/10.1007/s00440-002-0241-3

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  • Issue Date: March 2003

  • DOI: https://doi.org/10.1007/s00440-002-0241-3

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Keywords

  • Boundary Condition
  • Limit Theorem
  • Survival Probability
  • Dirichlet Boundary
  • Dirichlet Boundary Condition
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