Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems

the past hospitalization and its association with suicide attempts and ideation in patients with mdd and comparison with bmd (depressed type) group

چکیده ندارد.

Painlevé IV and degenerate Gaussian Unitary Ensembles

We consider those Gaussian Unitary Ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for the eigenvalues. In the simplest case where there is only one multiple eigenvalue t , this leads to orthogonal polynomials with the Hermite weight perturbed by a factor that has a multiple zero at t. We show through a pair of ladder operators, that the diag...

Global and Local Limit Laws for Eigenvalues of the Gaussian Unitary Ensemble and the Wishart Ensemble

Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble

Consider a n × n matrix from the Gaussian Unitary Ensemble (GUE). Given a finite collection of bounded disjoint real Borel sets (∆i,n, 1 ≤ i ≤ p), properly rescaled, and eventually included in any neighbourhood of the support of Wigner’s semi-circle law, we prove that the related counting measures (Nn(∆i,n), 1 ≤ i ≤ p), where Nn(∆) represents the number of eigenvalues within ∆, are asymptotical...

From Alternating Sign Matrices to the Gaussian Unitary Ensemble

The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the 6-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian Unitary Ensemble and the GUE-corners process.