Related papers: On Operator-valued Semicircular Random Variables
Motivated by a random matrix theory model from wireless communications, we define random operator-valued matrices as the elements of $L^{\infty-}(\Omega,{\mathcal F},{\mathbb P}) \otimes M_d({\mathcal A})$ where $(\Omega,{\mathcal…
It is a classical result in complex analysis that the class of functions that arise as the Cauchy transform of probability measures may be characterized entirely in terms of their analytic and asymptotic properties. Such transforms are a…
We study matrices whose entries are free or exchangeable noncommutative elements in some tracial $W^*$-probability space. More precisely, we consider operator-valued Wigner and Wishart matrices and prove quantitative convergence to…
We consider a transfer operator where two interacting cells carrying non-negative traits transfer a random fraction of their trait to each other. These transfers can lead to population having singular distributions in trait. We extend the…
We study of the connection between operator valued central limits for monotone, Boolean and free probability theory, which we shall call the arcsine, Bernoulli and semicircle distributions, respectively. In scalar-valued non-commutative…
Consider the $\mathcal{B}$-valued probability space $(\mathcal{A}, E, \mathcal{B})$, where $\mathcal{A}$ is a tracial von Neumann algebra. We extend the theory of operator valued free probability to the algebra of affiliated operators…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
In a 1999 paper, Bercovici and Pata showed that a natural bijection between the classically, free and Boolean infinitely divisible measures held at the level of limit theorems of triangular arrays. This result was extended to include…
In his article "On the free convolution with a semicircular distribution," Biane found very useful characterizations of the boundary values of the imaginary part of the Cauchy-Stieltjes transform of the free additive convolution of a…
This article proposes a co-variance operator for Banach valued random elements using the concept of $U$-statistic. We then study the asymptotic distribution of the proposed co-variance operator along with related large sample properties.…
In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an…
We address the question of a Berry-Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial…
How much unavoidable randomness is generated by a Positive Operator Valued Measure (POVM)? We address this question using two complementary approaches. First we study the variance of a real variable associated to the POVM outcomes. In this…
We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems respectively…
As more of topology's tools become popular in analyzing high dimensional data sets, the goal of understanding the underlying probabilistic properties of these tools becomes even more important. While much attention has been given to…
A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Holder solvability of semilinear equations and a strong similarity…
The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, with paying attention to the natural domains of these unbounded operators. The results are…
We give a spectral description of the semi-classical Schrodinger operator with a piecewise linear, complex valued potential. Moreover, using these results, we show how an arbitrarily small bounded perturbation of a non-self-adjoint operator…
We consider power means of independent and identically distributed (i.i.d.) non-integrable random variables. The power mean is an example of a homogeneous quasi-arithmetic mean. Under certain conditions, several limit theorems hold for the…
The weighted shift operators turn out to be extremely useful in supplying interesting examples of operators on Hilbert spaces. With a view to study a continuous analogue of weighted shifts, M. Embry and A. Lambert initiated the study of a…