| 研究開始時の研究の概要 |
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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