Analytic subordination for bi-free convolution
Operator Algebras
2018-01-11 v3 Probability
Abstract
In this paper we study some analytic properties of bi-free additive convolution, both scalar and operator-valued. We show that using properties of Voiculescu's subordination functions associated to free additive convolution of operator-valued distributions, simpler formulas for bi-free convolutions can be derived. We use these formulas in order to prove a result about atoms of bi-free additive convolutions.
Keywords
Cite
@article{arxiv.1702.01673,
title = {Analytic subordination for bi-free convolution},
author = {Serban Belinschi and Hari Bercovici and Yinzheng Gu and Paul Skoufranis},
journal= {arXiv preprint arXiv:1702.01673},
year = {2018}
}
Comments
Third version. Modifications and additions made in order to account for the existence of a zero set for the two-variable Cauchy transform