Rectangular random matrices. Related convolution

Details Rectangular random matrices. Related convolution Rectangular random matrices. Related convolution

2005-07-16

arxiv.org/abs/math/0507336v6

Mathematics

Operator Algebras

36 pages, to appear in PTRF

Scientific paper

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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