Related papers: Operator-valued spectral measures and large deviat…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
We consider the vector space of $n \times n$ matrices over $\mathbb C$, Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these operators are studied with respect to the underlying…
We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type $A_2$. We computed radial parts of its generators explicitly to obtain matrix-valued commuting…
This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…
In this paper, we study the local spectral properties of unilateral operator weighted shifts.
Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf H}-\lambda {\bf W}$,…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
We study the large deviations of sums of correlated random variables described by a matrix product ansatz, which generalizes the product structure of independent random variables to matrices whose non-commutativity is the source of…
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…
We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.
We study wave propagation in periodic and frequency dependent materials. The approach in this paper leads to spectral analysis of a quadratic operator pencil where the spectral parameter relates to the quasimomentum and the frequency is a…
The $W$-random graphs provide a flexible framework for modeling large random networks. Using the Large Deviation Principle (LDP) for $W$-random graphs from [9], we prove the LDP for the corresponding class of random symmetric…
In this paper, we consider a two-variable operator function that includes two weighted spectral geometric means, and show fundamental properties of the operator function. Moreover, it satisfies the Ando-Hiai type inequality under some…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
Probability measures (quasi probability mass), given in the form of integrals of Wigner function over areas of the underlying phase space, give rise to operator valued probability measures (OVM). General construction methods of OVMs, are…
In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach,…
We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small)…