On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions
Probability
2009-07-09 v5
Abstract
n this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko-Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.
Cite
@article{arxiv.0808.3938,
title = {On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions},
author = {Florent Benaych-Georges},
journal= {arXiv preprint arXiv:0808.3938},
year = {2009}
}
Comments
11 pages, 1 figure. To appear in Ann. Inst. Henri Poincar\'e Probab. Stat