English

Rectangular random matrices. Related convolution

Operator Algebras 2008-03-04 v6 Probability

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".

Keywords

Cite

@article{arxiv.math/0507336,
  title  = {Rectangular random matrices. Related convolution},
  author = {Florent Benaych-Georges},
  journal= {arXiv preprint arXiv:math/0507336},
  year   = {2008}
}

Comments

36 pages, to appear in PTRF