The spectral measures of random Jacobi matrices related to beta ensembles at high temperature and Dirichlet processes

Fumihiko Nakano, Hoang Dung Trinh, Khanh Duy Trinh

In a high temperature regime where ${\hat{I}}^{2}N\to 2c$, the empirical distribution of the eigenvalues of Gaussian beta ensembles, beta Laguerre ensembles and beta Jacobi ensembles converg…