Related papers: Random matrices: tail bounds for gaps between eige…
The tail-dependence compatibility problem is introduced. It raises the question whether a given $d\times d$-matrix of entries in the unit interval is the matrix of pairwise tail-dependence coefficients of a $d$-dimensional random vector.…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
This is a first paper by the authors dedicated to the distribution of eigenvalues for random perturbations of large bidiagonal Toeplitz matrices.
We observe returns of a simple random walk on a finite graph to a fixed node, and would like to infer properties of the graph, in particular properties of the spectrum of the transition matrix. This is not possible in general, but at least…
We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable.…
We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the…
In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…
The relative distance between eigenvalues of the compression of a not necessarily semibounded self-adjoint operator to a closed subspace and some of the eigenvalues of the original operator in a gap of the essential spectrum is considered.…
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…
The $t$-e.c. and pseudo-random property are typical properties of random graphs. In this note, we study the gap between them which has not been studied well. As a main result, we give the first explicit construction of infinite families of…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
The purpose of this note is twofold: firstly to improve the known results on variation of extreme eigenvalues of birth and death matrices and random walk matrices; and secondly to progress towards the solution of a thirty years old open…
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…
To consider a high-dimensional random process, we propose a notion about stochastic tensor-valued random process (TRP). In this work, we first attempt to apply a generic chaining method to derive tail bounds for all p-th moments of the…
In this note we give various characterizations of random walks with possibly different steps that have relatively large discrepancy from the uniform distribution modulo a prime p, and use these results to study the distribution of the rank…
We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.
We consider the probability of having two intervals (gaps) without eigenvalues in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We describe uniform asymptotics for the transition between a single large gap and…