確率論セミナー


2018/1/20(Sat)

14:30--15:20 数学教室 大セミナー室 (E404)

Trinh Khanh Duy

東北大学数理科学連携研究センター

Global spectral properties of Gaussian beta ensembles

Gaussian beta ensembles, as a generalization of Gaussian orthogonal/unitary/symplectic ensembles, were originally defined via the joint density function. Matrix models for them were introduced later by Dumitriu and Edelman in 2002. They are symmetric tridiagonal matrices, called Jacobi matrices, whose components are independent and are distributed according to specific distributions. In this talk, I will introduce some new results on the global spectral properties (empirical distributions and spectral measures) of Gaussian beta ensembles in the regime where the parameter beta is allowed to vary with the matrix size.