LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES

摘要

We use tridiagonal models to study the limiting behavior of β-Laguerre and β-Jacobi ensembles,focusing on the limiting behavior of the extremal eigenvalues and the central limit theorem for the two ensembles.For the central limit theorem of β-Laguerre ensembles,we follow the idea in[1]while giving a modified version for the generalized case.Then we use the total variation distance between the two sorts of ensembles to obtain the limiting behavior of β-Jacobi ensembles.