Heat Kernel Estimates for Jump Processes with Boundary Blow-up

This paper addresses a challenging problem in the study of Markov processes: estimating heat kernels for processes with jump kernels that blow up at the boundary of the state space. This is significant because it extends existing theory to a broader class of processes, including those arising in important applications like nonlocal Neumann problems and traces of stable processes. The key contribution is the development of new techniques to handle the non-uniformly bounded tails of the jump measures, a major obstacle in this area. The paper's results provide sharp two-sided heat kernel estimates, which are crucial for understanding the behavior of these processes.