Related papers: Infinite Random Matrix Theory, Tridiagonal Bordere…
Quantum entanglement under an extensive bipartition can reveal the critical boundary theory of a topological phase in the parameter space. In this study we demonstrate that the infinite-randomness fixed point for spin-1/2 degrees of freedom…
We assume that a finite set of moments of a random vector is given. Its underlying density is unknown. An algorithm is proposed for efficiently calculating Dirac mixture densities maintaining these moments while providing a homogeneous…
The linear finite element approximation of a general linear diffusion problem with arbitrary anisotropic meshes is considered. The conditioning of the resultant stiffness matrix and the Jacobi preconditioned stiffness matrix is investigated…
The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.
We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
We introduce the notion of a random matrix-valued multiplicative function, generalizing Rademacher random multiplicative functions to matrices. We provide an asymptotic for the second moment based on a linear recurrence property for…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We…
A new nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
We introduce and investigate a class of complex semi-infinite banded Toeplitz matrices satisfying the condition that the spectra of their principal submatrices accumulate onto a real interval when the size of the submatrix grows to…
We study large random matrices with i.i.d. entries conditioned to have prescribed row and column sums (margins), a problem connected to relative entropy minimization, Schr\"odinger bridges, contingency tables, and random graphs with given…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Toeplitz matrices are abundant in computational mathematics, and there is a rich literature on the development of fast and superfast algorithms for solving linear systems involving such matrices. Any Toeplitz matrix can be transformed into…
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the…
Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…
We show that the quantum Hamilton Jacobi approach to a class of quantum mechanical bound state problems and the Gaussian orthogonal ensemble of random matrix theory are equivalent. The Berry connection for both problems is identical to…
We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It…