On Operator-valued Semicircular Random Variables
Mohsen Soltanifar
TL;DR
This paper explores properties of operator-valued semicircular random variables, focusing on their Cauchy transforms and the nature of their distributions, including the presence of discrete parts.
Contribution
It introduces new insights into the representation of probability measures and the structure of distributions associated with operator-valued semicircular variables.
Findings
Representation of Cauchy transforms for compactly supported measures
Existence of nonzero discrete parts in distributions
Characterization of special properties of operator-valued semicircular variables
Abstract
In this paper, we discuss some special properties of operator- valued semicircular random variables including representation of the Cauchy transform of a compactly supported probability measure in terms of their operator-valued Cauchy transforms and existence of nonzero discrete part of their associated distributions.
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Taxonomy
TopicsRandom Matrices and Applications · Bayesian Methods and Mixture Models · Point processes and geometric inequalities