Local Universality in Biorthogonal Laguerre Ensembles

Universality for Orthogonal and Symplectic Laguerre-type Ensembles

We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) random matrix ensembles of Laguerre-type in the bulk of the spectrum as well as at the hard and soft spectral edges. They concern the appropriately rescaled kernels K n,β , correlation and cluster functions, gap probabilities and the distributions of the largest and smallest eigenvalues. Corresponding r...

A note on biorthogonal ensembles

Abstract. We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These systems are closely related to multiple orthogonal functions. It is known that the eigenvalue correlation functions of such ensembles can be written as a determinant of a kernel function. We show that the kernel...

Universality of General β-Ensembles

We prove the universality of the β-ensembles with convex analytic potentials and for any β > 0, i.e. we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian β-ensembles. AMS Subject Classification (2010): 15B52, 82B44

Edge Universality of Beta Ensembles

We prove the edge universality of the beta ensembles for any β > 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C 4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to ...

Biorthogonal Local Trigonometric Bases