Related papers: Precise asymptotics for the spectral radius of a l…

We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special…

We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive…

We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…

We consider a class of biased random walks on infinite graphs and present several general results on the spectral radius of biased random walk.

By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in…

We consider a one dimensional ballistic random walk evolving in a parametric independent and identically distributed random environment. We study the asymptotic properties of the maximum likelihood estimator of the parameter based on a…

In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…

We study the radius $R_T$ of a self-repellent fractional Brownian motion $\left\{B^H_t\right\}_{0\le t\le T}$ taking values in $\mathbb{R}^d$. Our sharpest result is for $d=1$, where we find that with high probability, \begin{equation*} R_T…

For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…

Let G be a graph with n vertices and mu(G) be the largest eigenvalue of the adjacency matrix of G. We study how large mu(G) can be when G does not contain cycles and paths of specified order. In particular, we determine the maximum spectral…

The spectral radius {\rho}(G) of a digraph G is the maximum modulus of the eigenvalues of its adjacency matrix. We present bounds on {\rho}(G) that are often tighter and are applicable to a larger class of digraphs than previously reported…

We show that the eigenvalue density of a product X=X_1 X_2 ... X_M of M independent NxN Gaussian random matrices in the large-N limit is rotationally symmetric in the complex plane and is given by a simple expression rho(z,\bar{z}) =…

We show that, under some general assumptions on the entries of a random complex $n \times n$ matrix $X_n$, the empirical spectral distribution of $\frac{1}{\sqrt{n}} X_n$ converges to the uniform law of an ellipsoid as $n$ tends to…

Let A be a p-variate real Wishart matrix on n degrees of freedom with identity covariance. The distribution of the largest eigenvalue in A has important applications in multivariate statistics. Consider the asymptotics when p grows in…

The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…

Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…

In [8], asymptotic expansion of the martingale with mixed normal limit was provided. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard…

We consider the family of N-dimensional real symmetric matrices H with random independent entries whose variance is determined by a function U((x-y)/b). In the limit of (relatively) narrow band width 1<<b<<N, we obtain explicitly first…

We consider the problem of determining the limiting spectral distribution for random matrices whose row distributions are permitted to have limited dependence. We assume mild moment conditions and give an extension of the…

We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…