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Rectangular random matrices. Related convolution

Florent Benaych-Georges
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Abstract

We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are asymtotically free with amalgamation over a subalgebra. Therefore we can define a "rectangular free convolution", linearized by cumulants and by an analytic integral transform, called the "rectangular R-transform".

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Florent Benaych-Georges. 2008-03-04. Rectangular random matrices. Related convolution. https://arxiv.org/abs/math/0507336

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