On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions

Florent Benaych-Georges

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 3, page 644-652
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Benaych-Georges, Florent. "On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions." Annales de l'I.H.P. Probabilités et statistiques 46.3 (2010): 644-652. <http://eudml.org/doc/240980>.

@article{Benaych2010,
abstract = {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.},
author = {Benaych-Georges, Florent},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {free probability; random matrices; free convolution; infinitely divisible laws; Marchenko–Pastur law; Marchenko-Pastur law},
language = {eng},
number = {3},
pages = {644-652},
publisher = {Gauthier-Villars},
title = {On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions},
url = {http://eudml.org/doc/240980},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Benaych-Georges, Florent
TI - On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 3
SP - 644
EP - 652
AB - 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.
LA - eng
KW - free probability; random matrices; free convolution; infinitely divisible laws; Marchenko–Pastur law; Marchenko-Pastur law
UR - http://eudml.org/doc/240980
ER -

References

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