Related papers: Non-backtracking Spectrum: Unitary Eigenvalues and…

We observe returns of a simple random walk on a finite graph to a fixed node, and would like to infer properties of the graph, in particular properties of the spectrum of the transition matrix. This is not possible in general, but at least…

A symmetric doubly stochastic matrix A is said to be determined by its spectra if the only symmetric doubly stochastic matrices that are similar to A are of the form $P^TAP$ for some permutation matrix P. The problem of characterizing such…

The aim of this paper is to study the existence of eigenvalues in the gap of the essential spectrum of the one-dimensional Dirac operator in the presence of a bounded potential. We employ a generalized variational principle to prove…

We prove interlacing inequalities between spectral minimal energies of metric graphs built on Dirichlet and standard Laplacian eigenvalues, as recently introduced in [Kennedy et al, arXiv:2005.01126]. These inequalities, which involve the…

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between…

In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman…

A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…

The traditional adjacency matrix of a mixed graph is not symmetric in general, hence its eigenvalues may be not real. To overcome this obstacle, several authors have recently defined and studied various Hermitian adjacency matrices of…

The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…

We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization,…

Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we…

We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a linear tree. The necessity was previously proven in 2014.…

The nonbacktracking matrix, and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as non-recurrent epidemics. Here we study the localization of NBC in infinite sparse…

On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap $\lambda_2 - \lambda_1$ is established, with a constant that depends…

We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically…

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…

M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint operators in gaps of the essential spectrum. Let $M$ be a…

We study spectral properties of the standard (also called Kirchhoff) Laplacian and the anti-standard (or anti-Kirchhoff) Laplacian on a finite, compact metric graph. We show that the positive eigenvalues of these two operators coincide…

We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…

We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-hermitian random-matrix models in the large-N limit. We apply this result to a number of non-hermitian random-matrix…