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