m at h . O A ] 1 7 N ov 2 00 6 RECTANGULAR RANDOM MATRICES , RELATED CONVOLUTION
نویسنده
چکیده
We characterize asymptotic collective behavior 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 asymptotically 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”.
منابع مشابه
M ar 2 00 8 RECTANGULAR RANDOM MATRICES , RELATED CONVOLUTION
We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all non commutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically fr...
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