Related papers: Spectral Theory of Sparse Non-Hermitian Random Mat…
We suggest that the spectral properties near zero virtuality of three dimensional QCD, follow from a Hermitean random matrix model. The exact spectral density is derived for this family of random matrix models both for even and odd number…
We present a numerical study of the spectrum of the Laplacian in an unbounded strip with PT-symmetric boundary conditions. We focus on non-Hermitian features of the model reflected in an unusual dependence of the eigenvalues below the…
Design of filters for graph signal processing benefits from knowledge of the spectral decomposition of matrices that encode graphs, such as the adjacency matrix and the Laplacian matrix, used to define the shift operator. For shift matrices…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…
The eigenvalues and eigenvectors of nonnormal matrices can be unstable under perturbations of their entries. This renders an obstacle to the analysis of numerical algorithms for non-Hermitian eigenvalue problems. A recent technique to…
Let $\mathcal A$ be the adjacency matrix of the Erd\H{o}s-R\'{e}nyi directed graph $\mathscr G(N,p)$. We denote the eigenvalues of $\mathcal A$ by $\lambda_1^{\cal A},...,\lambda^{\cal A}_N$, and $|\lambda_1^{\cal A}|=\max_i|\lambda_i^{\cal…
We study ensembles of sparse random block matrices generated from the adjacency matrix of a Erd\"os-Renyi random graph with $N$ vertices of average degree $Z$, inserting a real symmetric $d \times d$ random block at each non-vanishing…
We extensively explore the connections between time-like entanglement and non-hermitian density matrices in quantum many-body systems. We classify setups where we encounter non-hermitian density matrices into two types: one is due to causal…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
A theoretical model based on two-point scatterers is suggested to investigate scattering of partially coherent radiation by a non-Hermitian localized structure, invariant under the simultaneous symmetry operations of parity inversion and…
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
Computing pseudospectra of non-normal matrices is essential for understanding the stability and transient behavior of dynamical systems. Such analysis is critical in applications including fluid dynamics, control systems, and differential…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
In this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated Erd\H{o}s-R\'{e}nyi random graphs, we prove that the algorithm returns -- in polynomial time -- a…
We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…
We consider non-interacting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the DMRG method, by…
We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the…