Related papers: Distributions of Dirac Operator Eigenvalues

We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process…

In a system where chiral symmetry is spontaneously broken, the low energy eigenmodes of the continuum Dirac operator are extended. On the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes that affect…

We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-self-adjoint setting we establish the existence and…

System of Dirac fermions with random-varying mass is studied in detail. We reformulate the system by transfer-matrix formalism. Eigenvalues and wave functions are obtained numerically for various configurations of random telegraphic mass…

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a…

One dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the…

A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…

Macroscopic mechanical properties of polymers are determined by their microscopic molecular chain distribution. Due to randomness of these molecular chains, probability theory has been used to find their micro-states and energy…

Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields…

For a compact spin manifold $M$ isometrically embedded into Euclidean space, we derive the extrinsic estimates from above and below for eigenvalues of the Dirac operators, which depend on the second fundamental form of the embedding. We…

{Recently, we found that the correlation between the eigenvalues of random hermitean matrices exhibits universal behavior. Here we study this universal behavior and develop a diagrammatic approach which enables us to extend our previous…

We developed a microscopic approach to calculate the sample-to-sample fluctuations of transmission distribution in disordered conductors. This bridges between Green's function and random matrix theories of quantum transport. The results…

We consider the classical dynamics given by a one sided shift on the Bernoulli space of $d$ symbols. We study, on the space of H\"older functions, the eigendistributions of the Ruelle operator with a given potential. Our main theorem shows…

In this paper we find spectral properties in the large $N$ limit of Dirac operators that come from random finite noncommutative geometries. In particular for a Gaussian potential the limiting eigenvalue spectrum is shown to be universal…

In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact…

We consider families of finite quantum graphs of increasing size and we are interested in how eigenfunctions are distributed over the graph. As a measure for the distribution of an eigenfunction on a graph we introduce the entropy, it has…

We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide…

We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum,…

Fermionic theories with a vanishing chiral condensate (in the chiral limit) have recently attracted considerable interest; in particular variants of multi-flavour QCD are candidates for this behaviour. Here we consider the 2-flavour…

In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we…