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Universal approaches in random matrix theory

Research Project

Project/Area Number 24K06766
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionWaseda University

Principal Investigator

Trinh Khanh・Duy  早稲田大学, 理工学術院, 准教授(任期付) (00726127)

Project Period (FY) 2024-04-01 – 2029-03-31
Project Status Granted (Fiscal Year 2024)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2028: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2027: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2026: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2025: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2024: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywordsrandom matrix theory / beta ensembles / moment method / stochastic processes
Outline of Research at the Start

Three classical beta ensembles, Gaussian/Laguerre/Jacobi beta ensembles, are among the most studied random matrix models which are related to various fields of science. They can be approached by analyzing the joint density, reading off random tridiagonal matrix models and applying stochastic analysis tools to their dynamical versions (beta Dyson’s Brownian motions, beta Laguerre processes and beta Jacobi processes). This research aims to establish new spectral properties of the three beta ensembles and their related models and of (new) random matrix models arising in topology data analysis.

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Published: 2024-04-05   Modified: 2024-06-24  

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