Maurice Duits: Global fluctuations of biorthogonal ensembles via recurrence matrices

Abstract:

The moment generating function of linear statistics for a large class of biorthogonal ensembles can be written as the determinant of an nxn truncation of the exponential of a banded semi-infinite matrix. In this talk I will show how the band structure of the matrix can be exploited to find the asymptotic behavior for such determinants. These results can be used to prove concentration inequalities and Central Limit Theorems for the eigenvalue distribution of various random matrix models and random tilings of planar domains.