Prob/Stat Seminar

In this talk we will first discuss some of what is known about heat kernel estimates on manifolds with ends. By this we mean a finite number of manifolds satisfying two-sided Gaussian heat kernel estimates which are glued over a compact set. In the case of recurrent (parabolic) ends or in the case of manifolds with boundary with mixed Dirichlet and Neumann condition, the estimates depend on the harmonic profiles (positive harmonic functions) of the ends. Finally, we discuss recent progress toward obtaining heat kernel estimates in the case where the gluing set is non-compact. In particular, we give some hitting probability estimates. This is joint work with Laurent Saloff-Coste.

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