Related papers: Universal shocks in the Wishart random-matrix ense…
We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N…
We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the…
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…
Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…
We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the…
Number theorists have studied extensively the connections between the distribution of zeros of the Riemann $\zeta$-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices. It is interesting to…
We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…
We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a $N\times N$ random matrix taken from a $L$-deformed Chiral Gaussian Unitary Ensemble with an…
We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…
The eigenvalue statistics for complex $N \times N$ Wishart matrices $X_{r,s}^\dagger X_{r,s}$, where $ X_{r,s}$ is equal to the product of $r$ complex Gaussian matrices, and the inverse of $s$ complex Gaussian matrices, are considered. In…
It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related to orthogonal polynomials and their Cauchy…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
Based on the multivariate saddle point method we study the asymptotic behavior of the characteristic polynomials associated to Wishart type random matrices that are formed as products consisting of independent standard complex Gaussian and…
Recently, D. Wang has devised a new contour integral based method to simplify certain matrix integrals. Capitalizing on that approach, we derive a new expression for the probability density function (p.d.f.) of the joint eigenvalues of a…
Generalised uncorrelated Wishart matrices are formed out of rectangular standard Gaussian data matrices with a certain pattern of zero entries. Development of the theory in the real and complex cases has proceeded along separate line. For…
This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately…
This paper concentrates on asymptotic properties of determinants of some random symmetric matrices. If B_{n,r} is a n x r rectangular matrix and B_{n,r}' its transpose, we study det (B_{n,r}'B_{n,r}) when n,r tends to infinity with r/n \to…
We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components.…
This study derives a new property of the Wishart distribution when the degree-of-freedom and the size of the matrix parameter of the distribution grow simultaneoulsy. Particularly, the asymptotic normality of the product of four independent…
The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted…