Related papers: The polynomial method for random matrices
We analyse the limiting behavior of the eigenvalue and singular value distribution for random convolution operators on large (not necessarily Abelian) groups, extending the results by M. Meckes for the Abelian case. We show that for regular…
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
In this paper, we study the limiting distribution of the eigenvalues for random tridiagonal matrix models. The limiting distribution is well described by its moments. Here, an analytical approach allows us, as in the case of Wigner…
We consider ensembles of Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. We show the convergence of the Stieltjes transform towards the Stieltjes transform of the…
We show that any matrix-polynomial combination of free noncommutative random variables each having an algebraic law has again an algebraic law. Our result answers a question raised by a recent paper of Shlyakhtenko and Skoufranis. The…
We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any…
This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about…
We consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
Random tensors can be used to produce random matrices. This idea is, for instance, very natural when one studies random quantum states with the aim of exploring properties that are generically true, or true with some probability. We hereby…
We introduce a new technique to prove bounds for the spectral radius of a random matrix, based on using Jensen's formula to establish the zerofreeness of the associated characteristic polynomial in a region of the complex plane. Our…
We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of…
We consider a class of real random matrices with dependent entries and show that the limiting empirical spectral distribution is given by the Marchenko-Pastur law. Additionally, we establish a rate of convergence of the expected empirical…
In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between…