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

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

2008-08-28

arxiv.org/abs/0808.3938v5

Mathematics

Probability

11 pages, 1 figure. To appear in Ann. Inst. Henri Poincar\'e Probab. Stat

Scientific paper

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.

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