A note on existence of free Stein kernels
Operator Algebras
2018-11-08 v1 Functional Analysis
Probability
Abstract
Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is given by an explicit formula, and the other via free Poincar\'e inequalities. In particular, we show that unlike in the classical setting, free Stein kernels always exist. As corollaries, we derive new bounds on the rate of convergence in the free CLT, and a strengthening of a characterization of the semicircular law due to Biane.
Keywords
Cite
@article{arxiv.1811.02926,
title = {A note on existence of free Stein kernels},
author = {Guillaume Cébron and Max Fathi and Tobias Mai},
journal= {arXiv preprint arXiv:1811.02926},
year = {2018}
}
Comments
10 pages, comments are welcome