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Tokyo Probability Seminar
Seminar information archive ～05/23｜Next seminar｜Future seminars 05/24～
| 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
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.
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.
