• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2023 Fiscal Year Final Research Report

Analysis of random phenomena and its applications from the viewpoint of determinantal point processes

Research Project

  • PDF
Project/Area Number 18H01124
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionKyushu University

Principal Investigator

Shirai Tomoyuki  九州大学, マス・フォア・インダストリ研究所, 教授 (70302932)

Co-Investigator(Kenkyū-buntansha) 種村 秀紀  慶應義塾大学, 理工学部(矢上), 教授 (40217162)
香取 眞理  中央大学, 理工学部, 教授 (60202016)
Project Period (FY) 2018-04-01 – 2023-03-31
Keywords行列式点過程 / ガウス型解析関数 / ガウス型ローラン級数 / Weyl-Heisenberg点過程 / ワイヤレスネットワーク / ダイソンブラウン運動 / ランダム複体
Outline of Final Research Achievements

A stochastic model in which the probability distribution is described by a determinant, obtained by abstracting the repulsive nature of electrons (fermions), is called a determinant point process. It is known that the structure of the determinantal point process is hidden in many problems that are seemingly unrelated to electrons. In this study, we analyze random phenomena of such various determinantal point processes, especially focusing on asymptotic behavior and limit theorems, which are central issues in probability theory, and apply them to specific problems such as wireless networks.

Free Research Field

確率論

Academic Significance and Societal Importance of the Research Achievements

行列式点過程は、数理科学の中の多くの分野で現れる負の相関をもつランダム現象を記述する確率モデルである.行列式点過程の構造および性質を深く掘り下げることによりランダムな現象を解析した本研究は,数学としての確率論の一分野に貢献するとともに,機械学習やワイヤレスネットワークなど実世界の問題にも応用された例を鑑みると,未来のテクノロジーや社会の様々な分野で活用されるポテンシャルも期待される.

URL: 

Published: 2025-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi