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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Ratio limit theorem for parabolic horn-shaped domains


Authors: Pierre Collet, Servet Martinez and Jaime San Martin
Journal: Trans. Amer. Math. Soc. 358 (2006), 5059-5082
MSC (2000): Primary 60J65, 60J45, 35K05
Published electronically: June 13, 2006
MathSciNet review: 2231885
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Abstract: We prove that for horn-shaped domains of parabolic type, the ratio of the heat kernel at different fixed points has a limit when the time tends to infinity. We also give an explicit formula for the limit in terms of the harmonic functions.


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Additional Information

Pierre Collet
Affiliation: Centre de Physique Théorique, CNRS-UMR 7644 Ecole Polytechnique, 91128 Palaiseau Cedex, France
Email: Pierre.Collet@cpht.polytechnique.fr

Servet Martinez
Affiliation: CMM-DIM, UMI 2807-CNRS, Universidad de Chile, Casilla 170-3 Correo 3, Santiago, Chile
Email: smartine@dim.uchile.cl

Jaime San Martin
Affiliation: CMM-DIM, UMI 2807-CNRS, Universidad de Chile, Casilla 170-3 Correo 3, Santiago, Chile
Email: jsanmart@dim.uchile.cl

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03908-0
PII: S 0002-9947(06)03908-0
Keywords: Bessel process, Harnack inequality, heat kernel
Received by editor(s): September 2, 2004
Received by editor(s) in revised form: November 19, 2004
Published electronically: June 13, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.