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東京確率論セミナー
過去の記録 ～10/20｜次回の予定｜今後の予定 10/21～
| 開催情報 | 月曜日 16:00～17:30 数理科学研究科棟(駒場) 122号室 |
|---|---|
| 担当者 | 佐々田槙子、中島秀太（慶應義塾大学）、星野壮登（東京科学大学）、蛯名真久（東京科学大学） |
| セミナーURL | https://sites.google.com/view/tokyo-probability-seminar23/ |
2026年11月02日(月)
16:00-17:30 数理科学研究科棟(駒場) 122号室
15:20〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
大石 皐遥 氏 (京都大学)
Convergence rate estimates for semigroups and heat kernels associated with resistance forms
15:20〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
大石 皐遥 氏 (京都大学)
Convergence rate estimates for semigroups and heat kernels associated with resistance forms
[ 講演概要 ]
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.
