Tokyo Probability Seminar

Seminar information archive ~05/01Next seminarFuture seminars 05/02~

Date, time & place Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Makiko Sasada, Shuta Nakajima, Masato Hoshino

2024/09/30

16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Naotaka Kajino (Kyoto University)
Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
[ Abstract ]
This talk is aimed at presenting the results of the speaker's recent joint work (arXiv:2312.08546) with Mathav Murugan (University of British Columbia) on the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat kernel estimates. Our arguments rely on new results of independent interest such as sharp two-sided estimates and the volume doubling property of the harmonic measure, the existence of a continuous extension of the Na\"im kernel to the topological boundary, and the Doob--Na\"im formula identifying the Dirichlet form of the boundary trace process as the pure-jump Dirichlet form whose jump kernel with respect to the harmonic measure is exactly (the continuous extension of) the Na\"im kernel.