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Tokyo Probability Seminar
Seminar information archive ～12/25｜Next seminar｜Future seminars 12/26～
| Date, time & place | Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima, Masato Hoshino |
2025/10/20
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.
Ryo Oizumi (National Institute of Population and Social Security Research)
Fredholm Integral Equations and Eigenstructure: Genealogical Expansions via Non–Hilbert–Schmidt Solutions
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Ryo Oizumi (National Institute of Population and Social Security Research)
Fredholm Integral Equations and Eigenstructure: Genealogical Expansions via Non–Hilbert–Schmidt Solutions
[ Abstract ]
Fredholm integral equations play a central role in describing the long-term behavior of structured population models. In this talk, I present a determinant-free approach that constructs eigenfunctions through genealogical expansions, valid even beyond the Hilbert–Schmidt setting. The expansion is closely related to taboo probabilities in Markov chains, allowing eigenfunctions to be interpreted as cumulative ancestral contributions. As an application, I discuss age-structured branching processes and show how quantities such as expected generation counts and reproduction numbers naturally arise from the eigenvalue problem. This perspective highlights how eigenstructure encodes genealogical memory and opens connections between population dynamics, probability theory, and evolutionary processes.
Fredholm integral equations play a central role in describing the long-term behavior of structured population models. In this talk, I present a determinant-free approach that constructs eigenfunctions through genealogical expansions, valid even beyond the Hilbert–Schmidt setting. The expansion is closely related to taboo probabilities in Markov chains, allowing eigenfunctions to be interpreted as cumulative ancestral contributions. As an application, I discuss age-structured branching processes and show how quantities such as expected generation counts and reproduction numbers naturally arise from the eigenvalue problem. This perspective highlights how eigenstructure encodes genealogical memory and opens connections between population dynamics, probability theory, and evolutionary processes.
