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