Mathematics Seminar Series: Probability

Title: Heat kernel estimates for Dirichlet forms degenerate at the boundary.

Abstract: In this talk, we discuss estimates on the heat kernels of discontinuous symmetric Markov processes including ones with jump kernels degenerate at the boundary. Depending on the regions where the parameters belong, the heat kernels estimates have different forms. There are now forms qualitatively different from all previously known heat kernel estimates. We also discuss the processes killed either by a critical potential or upon hitting the boundary. Their heat kernel estimates have the approximate factorization property with survival probabilities decaying as a power of the distance to the boundary, where the power depends on the critical potential. This talk is based on joint papers with Soobin Cho, Renming Song and Zoran Vondra\v{c}ek.