Distribution of eigenvalues of random operators and related limit theorems

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400148
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Keio University
• Principal Investigator: MINAMI Nariyuki 慶應義塾大学, 医学部(日吉), 教授 (10183964)
• Co-Investigator(Renkei-kenkyūsha): NAKANO Fumihiko 学習院大学, 理学部, 教授 (10291246) ; UEKI Naomasa 京都大学, 人間・環境学研究科, 教授 (80211069)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: ランダム作用素 / スペクトル統計 / 一般化シュレーディンガー作用素 / 感染症数理モデル / 世代間隔

Outline of Final Research Achievements

(1) 1-dimensional Schroedinger operator H with decaying white noise potential is considered, and its spectral properties are determined when the decaying factor is square integrable. Also, the property of a part of the spectrum of H is determined when the decaying factor is not square integrable.
(2) Based on a mathematical model which incorporates a hypothesis that adult males and females are mildly segregated in their social life, it is shown that a condition is ready for the 2013 rubella outbreak in Japan. By another mathematical model, possible consequences of the rubella vaccination limited to schoolgirls were shown.
(3) A stochastic model is constructed in order to clarify the notion of "generation interval" in infectious disease epidemiology.

Free Research Field

確率論とその数理物理学および数理疫学への応用