相关论文: A note on eigenvalues and singular values of varia…

The purpose of this paper is to describe asymptotic formulas for determinants of a sum of finite Toeplitz and Hankel matrices with singular generating functions. The formulas are similar to those of the analogous problem for finite Toeplitz…

Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that…

We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to random normal matrices with complex spectra: (i) the…

Consider random symmetric Toeplitz matrices $T_{n}=(a_{i-j})_{i,j=1}^{n}$ with matrix entries $a_{j}, j=0,1,2,...,$ being independent real random variables such that \be \mathbb{E}[a_{j}]=0, \ \ \mathbb{E}[|a_{j}|^{2}]=1 \ \ \textrm{for}\,\…

This work deals with the isogeometric Galerkin discretization of the eigenvalue problem related to the Laplace operator subject to homogeneous Dirichlet boundary conditions on bounded intervals. This paper uses GLT theory to study the…

Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary…

Starting from the definition of an $n\times n$ $g$-Toeplitz matrix, $T_{n,g}(u)=\left[\widehat{u}_{r-gs}\right]_{r,s=0}^{n-1},$ where $g$ is a given nonnegative parameter, $\{\widehat{u}_{k}\}$ is the sequence of Fourier coefficients of the…

We study averages of multiplicative eigenvalue statistics in ensembles of orthogonal Haar distributed matrices, which can alternatively be written as Toeplitz+Hankel determinants. We obtain new asymptotics for symbols with Fisher-Hartwig…

Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d random variables chosen from a fixed probability distribution p of mean 0, variance 1 and finite higher moments. Previous work [BDJ,HM] showed that the…

Let $G=G(n,p_n)$ be a homogeneous Erd\"os-R\'enyi graph, and $A$ its adjacency matrix with eigenvalues $\lambda_1(A) \geq \lambda_2(A) \geq ... \geq \lambda_n(A).$ Local laws have been used to show that $lambda_2(A)$ can exhibit…

Let $A$ be an infinite Toeplitz matrix with a real symbol $f$ defined on $[-\pi, \pi]$. It is well known that the sequence of spectra of finite truncations $A_N$ of $A$ converges to the convex hull of the range of $f$. Recently, Levitin and…

In this article we characterize measure theoretical eigenvalues of Toeplitz Bratteli-Vershik minimal systems of finite topological rank which are not associated to a continuous eigenfunction. Several examples are provided to illustrate the…

Let $(\varepsilon_{t})_{t>0}$ be a sequence of independent real random vectors of $p$-dimension and let $X_T= \sum_{t=s+1}^{s+T}\varepsilon_t\varepsilon^T_{t-s}/T$ be the lag-$s$ ($s$ is a fixed positive integer) auto-covariance matrix of…

We derive sharp approximation error bounds for inverse block Toeplitz matrices associated with multivariate long-memory stationary processes. The error bounds are evaluated for both column and row sums. These results are used to prove the…

It was shown in a series of recent publications that the eigenvalues of $n\times n$ Toeplitz matrices generated by so-called simple-loop symbols admit certain regular asymptotic expansions into negative powers of $n+1$. On the other hand,…

We study the limiting behavior of singular values of a lag-$\tau$ sample auto-correlation matrix $\bf{R}_{\tau}^{\epsilon}$ of error term $\epsilon$ in the high-dimensional factor model. We establish the limiting spectral distribution (LSD)…

We apply time-dependent Ginzburg Landau (TDGL) numerical simulations to study the finite frequency electrodynamics of superconductors subjected to intense rf magnetic field. Much recent TDGL work has focused on spatially uniform external…

In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory…

This thesis is based on joint work with Jon Keating [FK21], Tom Claeys and Jon Keating [CFK23], and Isao Sauzedde [FS22], and is concerned with establishing and studying connections between random matrices and log-correlated fields. This is…

Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal…