相关论文: Gap probabilities and densities of extreme eigenva…

We compute exact asymptotic of the statistical density of random matrices belonging to invariant random matrices ensemble (RMT) orthogonal, unitary and symplectic ensembles, where all its eigenvalues lie within the interval $[\sigma,…

We study two types of random matrix ensembles that emerge when considering the same probability measure on partitions. One is the Meixner ensemble with a hard wall and the other are two families of unitary matrix models, with weight…

We consider random n\times n matrices of the form (XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}, where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are…

We propose a method based on the Wang-Landau algorithm to numerically generate the spectral densities of random matrix ensembles. The method employs Dyson's log-gas formalism for random matrix eigenvalues and also enables one to…

We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumption of invariance. These include Gaussian matrices with…

We study the gaps between consecutive singular values of random rectangular matrices. Specifically, if $M$ is an $n \times p$ random matrix with independent and identically distributed entries and $\Sigma$ is a $n \times n$ deterministic…

We consider the squared singular values of the product of $M$ standard complex Gaussian matrices. Since the squared singular values form a determinantal point process with a particular Meijer G-function kernel, the gap probabilities are…

An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…

In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…

For the correlated Gaussian Wishart ensemble we compute the distribution of the smallest eigenvalue and a related gap probability.We obtain exact results for the complex (\beta=2) and for the real case (\beta=1). For a particular set of…

We develop a method to compute the moments of the eigenvalue densities of matrices in the Gaussian, Laguerre and Jacobi ensembles for all the symmetry classes beta = 1,2, 4 and finite matrix dimension n. The moments of the Jacobi ensembles…

This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…

Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…

We discuss non-Gaussian random matrices whose elements are random variables with heavy-tailed probability distributions. In probability theory heavy tails of the distributions describe rare but violent events which usually have dominant…

Wishart random matrices are often used to model multivariate systems in physics, finance, biology and wireless communication. Extreme value statistics, such as those of the smallest eigenvalue, can be used to test the accuracy of the model.…

We present novel understandings of the Gamma-Poisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the…

Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…

Using the proposed by us thinning approach to describe extreme matrices, we find an explicit exponentiation formula linking classical extreme laws of Fr\'echet, Gumbel and Weibull given by Fisher-Tippet-Gnedenko classification and free…

We present a large deviation principle at speed N for the largest eigenvalue of some additively deformed Wigner matrices. In particular this includes Gaussian ensembles with full-rank general deformation. For the non-Gaussian ensembles, the…