Related papers: Asymptotically Pseudo-Independent Matrices
We prove that independent families of permutation invariant random matrices are asymptotically free over the diagonal, both in probability and in expectation, under a uniform boundedness assumption on the operator norm. We can relax the…
We consider the problem of generating pseudo-random matrices based on the similarity of their spectra to Wigner's semicircular law. We introduce the notion of an r-independent pseudo-Wigner matrix ensemble and prove closeness of the spectra…
We show that the operatorial framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called…
A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
In this review we summarise recent results for the complex eigenvalues and singular values of finite products of finite size random matrices, their correlation functions and asymptotic limits. The matrices in the product are taken from…
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…
Sergey Pinchuk discovered a class of pairs of real polynomials in two variables that have a nowhere vanishing Jacobian determinant and define maps of the real plane to itself that are not one-to-one. This paper describes the asymptotic…
Asymptotics deviation probabilities of the sum S n = X 1 + $\times$ $\times$ $\times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated , in particular when X 1 is not…
Suppose that A_1,\dots, A_N are independent random matrices whose atoms are iid copies of a random variable \xi of mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when \xi is gaussian then…
The paper investigates the asymptotic behavior of (non-normalized) traces of certain classes of matrices with non-commutative random variables as entries. We show that, unlike in the commutative framework, the asymptotic behavior of…
The asymptotic freeness of independent unitarily invariant $N\times N$ random matrices holds in expectation up to $O(N^{-2})$. An already known consequence is the infinitesimal freeness in expectation. We put in evidence another consequence…
In this paper we study the asymptotic behavior for large argument of a family of solutions of the Painlev\'e equation P$_{\rm VI} arising in the context of Random Matrix Theory [1]. We show this family of solutions are uniquely determined…
This article demonstrates how recent developments in the theory of empirical processes allow us to construct a new family of asymptotically distribution-free smooth tests. Their distribution-free property is preserved even when the…
We introduce a class of paired binary matrices called admixed arrays, which arise in analyses of large-scale genetic data and can be viewed as weighted edge colorings of complete bipartite graphs. This combinatorial structure gives rise to…
We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one. We prove the existence of the full asymptotic expansions of these spherical integrals and derive the first and the second term in…
Disjunct matrices, also known as cover-free families and superimposed codes, are combinatorial arrays widely used in group testing. Among their variants, those that satisfy an additional combinatorial property called inclusiveness form a…
We study products of functions evaluated at self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such products and control the fluctuations. We focus on…
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…
We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…