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Tokyo Probability Seminar
Seminar information archive ～06/26｜Next seminar｜Future seminars 06/27～
| Date, time & place | Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima (Keio Univ.), Masato Hoshino (Science Tokyo), Masahisa Ebina (Science Tokyo) |
2026/06/29
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Ryoichiro Noda (Waseda University)
Fine geometry of collision measures
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Ryoichiro Noda (Waseda University)
Fine geometry of collision measures
[ Abstract ]
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.
