Determinantal processes and their generalizations

2017 Fiscal Year Final Research Report

• Project/Area Number: 26287019
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu 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): 脇 隼人 九州大学, マス・フォア・インダストリ研究所, 准教授 (00567597) ; 種村 秀紀 千葉大学, 大学院理学研究院, 教授 (40217162) ; 香取 眞理 中央大学, 理工学部, 教授 (60202016)
• Co-Investigator(Renkei-kenkyūsha): MIYOSHI Naoto 東京工業大学, 情報理工学院, 教授 (20263121)
• Research Collaborator: OSADA Hirofumi 九州大学, 大学院数理学研究院, 教授 (20177207)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 行列式過程 / ギニブル点過程 / 再生核ヒルベルト空間 / パーム測度 / ワイヤレスネットワーク / 代数的力学系 / SLE / Dysonモデル

Outline of Final Research Achievements

Determinantal point processes are one of the most important models of describing several phenomena that exhibit repulsion. We investigate theoretical aspects and also application aspects of determinantal point processes and their generalization. For example, we estimate the Signal-to-Interference-Ratio for the wireless network whose base stations are configurated by Ginibre point process, which is one of the most important determinantal point processes and has been used for the study of random matrices in physics.

Free Research Field

確率論