Related papers: Infinite Random Matrix Theory, Tridiagonal Bordere…
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}\,\…
We consider matrices on infinite trees which are universal covers of Jacobi matrices on finite graphs. We are interested in the question of the existence of sequences of finite covers whose normalized eigenvalue counting measures converge…
The purpose of this work is to bound sofic topological entropy of Toeplitz systems over residually finite groups and to prove the Krieger Theorem about attaining arbitrary entropy by the Toeplitz systems. To achieve these results, we…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
In this paper, we study the condition number of a random Toeplitz matrix. Since a Toeplitz matrix is a diagonal constant matrix, its rows or columns cannot be stochastically independent. This situation does not permit us to use the classic…
We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader…
In this paper, we consider the problem of seriation of a permuted structured matrix based on noisy observations. The entries of the matrix relate to an expected quantification of interaction between two objects: the higher the value, the…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem…
In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. \ We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in…
Bordered and framed Toeplitz/Hankel determinants have the same structure as Toeplitz/Hankel determinants except in small number of matrix rows and/or columns. We review these structured determinants and their connections to orthogonal…
Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of $L$-functions; this correspondence has allowed RMT to successfully predict many number theoretic behaviors. However there…
Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…
The stories told in this paper are dealing with the solution of finite, infinite, and biinfinite Toeplitz-type systems. A crucial role plays the off-diagonal decay behavior of Toeplitz matrices and their inverses. Classical results of…
In this article, we focus on tridiagonal Toeplitz Hermitian matrices, which fulfill the requirement of a valid Hamiltonian often used in Quantum Information. We investigate the behavior of such matrices to pursue the dynamics of quantum…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
In this manuscript it is considered the eigenvalues $\lambda_j$ of a random tridiagonal Toeplitz matrix $T$. We study the asymptotic behavior of the joint distribution of $({|{\lambda}|_{\min} ,|{\lambda}|_{\max}})$. From this, we obtain…
We investigate the joint convergence of independent random Toeplitz matrices with complex input entries that have a pair-correlation structure, along with deterministic Toeplitz matrices and the backward identity permutation matrix.…
We consider a class of linear matrix equations involving semi-infinite matrices which have a quasi-Toeplitz structure. These equations arise in different settings, mostly connected with PDEs or the study of Markov chains such as random…
This paper addresses the challenge of Toeplitz covariance matrix estimation from partial entries of random quantized samples. To balance trade-offs among the number of samples, the number of entries observed per sample, and the data…