Related papers: Universality for the conjugate gradient and MINRES…
We consider the spectrum of the Sample Covariance matrix $\mathbf{A}_N:= \frac{\mathbf{X}_N \mathbf{X}_N^*}{N}, $ where $\mathbf{X}_N$ is the $P\times N$ matrix with i.i.d. half-heavy tailed entries and $\frac{P}{N}\to y>0$ (the entries of…
A Central Limit Theorem for linear combinations of iterates of an inner function is proved. The main technical tool is Aleksandrov Desintegration Theorem for Aleksandrov-Clark measures.
Let $(\tau_n)$ be a sequence of toral automorphisms $\tau_n : x \rightarrow A_n x \hbox{mod}\ZZ^d$ with $A_n \in {\cal A}$, where ${\cal A}$ is a finite set of matrices in $SL(d, \mathbb{Z})$. Under some conditions the method of…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
Lacunary function systems of type $(f(M_nx))_{n\geq 1}$ for periodic functions $f$ and sequences of fast-growing matrices $(M_n)_{n\geq 1}$ exhibit many properties of independent random variables like satisfying the Central Limit Theorem or…
We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of Goncharov for the number of cycles of a single random…
This note presents some central limit theorems for the eigenvalue counting function of Wigner matrices in the form of suitable translations of results by Gustavsson and O'Rourke on the limiting behavior of eigenvalues inside the bulk of the…
We study the eigenvalues of the covariance matrix $\frac{1}{n}M^*M$ of a large rectangular matrix $M=M_{n,p}=(\zeta_{ij})_{1\leq i\leq p;1\leq j\leq n}$ whose entries are i.i.d. random variables of mean zero, variance one, and having finite…
A new definition of the $\mathcal{H}_2$ norm for linear switched systems is introduced. It is based on appropriately defined time-domain kernels, or equivalently, on infinite controllability and observability Gramian matrices. Furthermore,…
We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic…
GMRES is a popular Krylov subspace method for solving linear systems of equations involving a general non-Hermitian coefficient matrix. The conventional bounds on GMRES convergence involve polynomial approximation problems in the complex…
We give an algorithm that generates a uniformly random contingency table with specified marginals, i.e. a matrix with non-negative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics.…
The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate…
We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N^D independent, identically distributed, complex random variables converges in distribution in the large N…
We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanczos quadrature, two widely used methods for these tasks. Our…
We prove universality for cokernels of random integral matrices with symmetries via an approach different from the classical surjection moment method introduced by Wood (arXiv:1402.5149). In the symmetric case, we reprove Hodges'…
We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…
We prove a version of the multidimensional Fourth Moment Theorem for chaotic random vectors, in the general context of diffusion Markov generators. In addition to the usual componentwise convergence and unlike the infinite-dimensional…
For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…
The distribution of descents in fixed conjugacy classes of $S_n$ has been studied, and it is shown that its moments have interesting properties. Kim and Lee showed, by using Curtiss' theorem and moment generating functions, how to prove a…