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Tokyo Probability Seminar
Seminar information archive ～10/20｜Next seminar｜Future seminars 10/21～
| Date, time & place | Monday 16:00 - 17:30 122Room #122 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima (Keio Univ.), Masato Hoshino (Science Tokyo), Masahisa Ebina (Science Tokyo) |
2026/11/02
16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Koyo Oishi (Kyoto University)
Convergence rate estimates for semigroups and heat kernels associated with resistance forms
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Koyo Oishi (Kyoto University)
Convergence rate estimates for semigroups and heat kernels associated with resistance forms
[ Abstract ]
In this talk, we present quantitative convergence rates for stochastic processes associated with resistance forms. While the qualitative convergence of heat kernels and semigroups under the Gromov-Hausdorff-vague convergence of underlying measured resistance metric spaces has been investigated previously, their quantitative convergence rates have remained unexplored. We establish explicit convergence rates for the associated semigroups and heat kernels under the assumptions of measure regularity and lower resistance estimates. Furthermore, we introduce a new metric that induces the Gromov-Hausdorff-vague topology and is convenient for obtaining quantitative estimates. As applications of our main results, we present several examples, including the Sierpinski gasket and the Bouchaud trap model. In some of these examples, we obtain the first quantitative estimates for previously known convergence results, while in others, we improve existing estimates.
In this talk, we present quantitative convergence rates for stochastic processes associated with resistance forms. While the qualitative convergence of heat kernels and semigroups under the Gromov-Hausdorff-vague convergence of underlying measured resistance metric spaces has been investigated previously, their quantitative convergence rates have remained unexplored. We establish explicit convergence rates for the associated semigroups and heat kernels under the assumptions of measure regularity and lower resistance estimates. Furthermore, we introduce a new metric that induces the Gromov-Hausdorff-vague topology and is convenient for obtaining quantitative estimates. As applications of our main results, we present several examples, including the Sierpinski gasket and the Bouchaud trap model. In some of these examples, we obtain the first quantitative estimates for previously known convergence results, while in others, we improve existing estimates.
