On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions
Résumé
In this paper, we prove a result linking the square and the rectangular R-transforms, which consequence is a surprising relation between the square and rectangular free convolutions, involving the Marchenko-Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of Voiculescu's free additive and multiplicative convolutions are given.
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