Universal approaches in random matrix theory

• Project/Area Number: 24K06766
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Waseda 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: ¥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)
• Keywords: random 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.