Hermite and Laguerre polynomials and matrix-valued stochastic.
How tight is Hadamard's bound?
Integral representations for multiple Hermite and multiple Laguerre polynomials
We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
Jacobians of certain transformations of singular matrices
In this study various Jacobians of transformations of singular random matrices are found. An alternative proof of Uhlig's first conjecture (Uhlig (1994)) is proposed. Furthermore, we propose various extensions of this conjecture under different singularities. Finally, an application of the theory of singular distributions is discussed.
Jucys-Murphy elements and the unitary Weingarten function
We describe an approach to the unitary Weingarten function based on the JM elements of symmetric group algebras. When combined with previously known properties of the Weingarten function, this gives a surprising connection with the Moebius function of the lattice of noncrossing partitions.
Large deviations and stochastic calculus for large random matrices.
Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles.
Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices
Large time asymptotics of growth models on space-like paths. I: Push ASEP.
Limit distributions of many-particle spectra and q-deformed Gaussian variables
We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q-deformed Gaussian distribution with the deformation parameter q depending on the fraction k/√n. The family of q-deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner [Wig1,...
Limiting spectral distribution of circulant type matrices with dependent inputs.
Limiting spectral distribution of XX' matrices
The methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices includes the well-known moment method which invokes the trace formula. Its success has been demonstrated in several types of matrices such as the Wigner matrix and the sample covariance matrix. In a recent article Bryc, Dembo and Jiang [Ann. Probab.34 (2006) 1–38] establish the LSD for random Toeplitz and Hankel matrices using the moment method. They perform the necessary counting of terms in the...
Localisation pour des opérateurs de Schrödinger aléatoires dans : un modèle semi-classique
Dans , nous démontrons un résultat de localisation exponentielle pour un opérateur de Schrödinger semi-classique à potentiel périodique perturbé par de petites perturbations aléatoires indépendantes identiquement distribuées placées au fond de chaque puits. Pour ce faire, on montre que notre opérateur, restreint à un intervalle d’énergie convenable, est unitairement équivalent à une matrice aléatoire infinie dont on contrôle bien les coefficients. Puis, pour ce type de matrices, on prouve un résultat...
Localization and delocalization for heavy tailed band matrices
We consider some random band matrices with band-width whose entries are independent random variables with distribution tail in . We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when , the largest eigenvalues have order , are asymptotically distributed as a Poisson process and their associated eigenvectors are essentially carried by two coordinates (this phenomenon has already been remarked for full matrices by Soshnikov...
Lower order terms for the one-level densities of symmetric power L-functions in the level aspect
Matrices aléatoires : statistique asymptotique des valeurs propres
Matrix-Variate Statistical Distributions and Fractional Calculus
MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthdayA connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions of fractional...
Moderate deviations for the spectral measure of certain random matrices
Moderate deviations for traces of words in a mult-matrix model.
Moderate deviations in a random graph and for the spectrum of Bernoulli random matrices.