Related papers: Singular values of large non-central random matric…

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…

We consider a Gaussian rotationally invariant ensemble of random real totally symmetric tensors with independent normally distributed entries, and estimate the largest eigenvalue of a typical tensor in this ensemble by examining the rate of…

We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…

This paper studies the asymptotic behavior of eigenvalues of random abelian G-circulant matrices, that is, matrices whose structure is related to a finite abelian group G in a way that naturally generalizes the relationship between…

For any family of $N\times N$ random matrices $(\mathbf{A}_k)_{k\in K}$ which is invariant, in law, under unitary conjugation, we give general sufficient conditions for central limit theorems for random variables of the type…

We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a…

We study the $k$-core of a random (multi)graph on $n$ vertices with a given degree sequence. In our previous paper [Random Structures Algorithms 30 (2007) 50--62] we used properties of empirical distributions of independent random variables…

Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained…

Consider Ginibre's ensemble of $N \times N$ non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance $\frac{1}{N}$. As $N \uparrow \infty$ the normalized counting measure of the…

Let M be an arbitrary Hermitian matrix of order n, and k be a positive integer less than or equal to n. We show that if k is large, the distribution of eigenvalues on the real line is almost the same for almost all principal submatrices of…

We consider a multivariate linear response regression in which the number of responses and predictors is large and comparable with the number of observations, and the rank of the matrix of regression coefficients is assumed to be small. We…

An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions…

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

We study the fluctuations of the eigenvalues of real valued large centrosymmetric random matrices via its linear eigenvalue statistic. This is essentially a central limit theorem (CLT) for sums of dependent random variables. The dependence…

We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…

We provide some asymptotic theory for the largest eigenvalues of a sample covariance matrix of a p-dimensional time series where the dimension p = p_n converges to infinity when the sample size n increases. We give a short overview of the…

We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…

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…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…

We consider the probability of two large gaps (intervals without eigenvalues) in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We determine the multiplicative constant in the asymptotics. We also provide the…