In 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.
Publié le : 2010-08-15
Classification:
Free probability,
Random matrices,
Free convolution,
Infinitely divisible laws,
Marchenko–Pastur law,
46L54,
15A52
@article{1281100393,
author = {Benaych-Georges, Florent},
title = {On a surprising relation between the Marchenko--Pastur law, rectangular and square free convolutions},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 644-652},
language = {en},
url = {http://dml.mathdoc.fr/item/1281100393}
}
Benaych-Georges, Florent. On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 644-652. http://gdmltest.u-ga.fr/item/1281100393/