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東京確率論セミナー
過去の記録 ～10/15｜次回の予定｜今後の予定 10/16～
| 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（明治大学）、星野壮登（東京科学大学） |
| セミナーURL | https://sites.google.com/view/tokyo-probability-seminar23/ |
次回の予定
2025年10月20日(月)
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 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。
大泉 嶺 氏 (国立社会保障・人口問題研究所 (厚生労働省))
Fredholm Integral Equations and Eigenstructure: Genealogical Expansions via Non–Hilbert–Schmidt Solutions
15:15〜 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。
大泉 嶺 氏 (国立社会保障・人口問題研究所 (厚生労働省))
Fredholm Integral Equations and Eigenstructure: Genealogical Expansions via Non–Hilbert–Schmidt Solutions
[ 講演概要 ]
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.
