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東京確率論セミナー
過去の記録 ～06/26｜次回の予定｜今後の予定 06/27～
| 開催情報 | 月曜日 16:00～17:30 数理科学研究科棟(駒場) 126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06月29日(月)
16:00-17:30 数理科学研究科棟(駒場) 126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。
野田 涼一郎 氏 (早稲田大学)
Fine geometry of collision measures
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。
野田 涼一郎 氏 (早稲田大学)
Fine geometry of collision measures
[ 講演概要 ]
Given several independent stochastic processes, their collision measure is a random measure that records when and where they collide. In this talk, I will discuss fine geometric properties of collision measures for independent Markov processes on metric measure spaces. Under standard heat kernel estimates, we identify the local dimensions of the temporal and spatial marginals of the collision measure. We also determine the Hausdorff dimensions of their supports, as well as those of the corresponding sets of collision times and collision sites. Finally, we study logarithmic limsup gauges describing typical and thick collision times and sites.
Given several independent stochastic processes, their collision measure is a random measure that records when and where they collide. In this talk, I will discuss fine geometric properties of collision measures for independent Markov processes on metric measure spaces. Under standard heat kernel estimates, we identify the local dimensions of the temporal and spatial marginals of the collision measure. We also determine the Hausdorff dimensions of their supports, as well as those of the corresponding sets of collision times and collision sites. Finally, we study logarithmic limsup gauges describing typical and thick collision times and sites.
