Related papers: Spectral gap estimates for some block matrices

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…

The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…

The spectral problem for matrices with a block-hierarchical structure is often considered in context of the theory of complex systems. In the present article, a new class of matrices with a block-rectangular non-symmetric hierarchical…

The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these…

We are going to study the limiting spectral measure of fixed dimensional Hermitian block-matrices with large dimensional Wigner blocks. We are going also to identify the limiting spectral measure when the Hermitian block-structure is…

Some constructions and bounds on the sizes of semiovals contained in the Hermitian curve are given. A construction of an infinite family of 2-blocking sets of the Hermitian curve is also presented.

We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for pumpkin chains with number of edges tending to infinity.

We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…

For the almost Mathieu operator with a small coupling constant, for a series of spectral gaps, we describe the asymptotic locations of the gaps and get lower bounds for their lengths. The results are obtained by analysing a monodromy…

We present an algorithm for reliably and systematically proving the existence of spectral gaps in Hamiltonians with quasicrystalline order, based on numerical calculations on finite domains. We apply this algorithm to prove that the…

Let $A$ be a $n\times n$ complex Hermitian matrix and let $\lambda(A)=(\lambda_1,\ldots,\lambda_n)\in \mathbb{R}^n$ denote the eigenvalues of $A$, counting multiplicities and arranged in non-increasing order. Motivated by problems arising…

We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…

Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…

Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks

The empirical spectral distribution of Hermitian $K \times K$-block random matrices converges to a deterministic density on the real line with a potential atom at the origin as the dimension of the blocks tends to infinity. In this model…

When a projection of a symmetric or Hermitian matrix to the positive semidefinite cone is computed approximately (or to working precision on a computer), a natural question is to quantify its accuracy. A straightforward bound invoking…

We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.

Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the so called gap of a finite metric space of strict…

In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…

We provide a detailed description of the maps associated with spectral interlacing, for rank one perturbations and bordering of symmetric and Hermitian matrices. The arguments rely on standard techniques of nonlinear analysis.