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arXiv · 0808.3938

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

Florent Benaych-Georges
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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.

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Florent Benaych-Georges. 2009-07-09. On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions. https://arxiv.org/abs/0808.3938

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