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Pré-Publication, Document De Travail Année : 2005

Rectangular random matrices, related convolution

Résumé

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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Dates et versions

hal-00007541 , version 1 (16-07-2005)
hal-00007541 , version 2 (04-12-2005)
hal-00007541 , version 3 (17-11-2006)
hal-00007541 , version 4 (11-06-2007)
hal-00007541 , version 5 (22-01-2008)
hal-00007541 , version 6 (04-03-2008)

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Florent Benaych-Georges. Rectangular random matrices, related convolution. 2005. ⟨hal-00007541v1⟩
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