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On a surprising relation between rectangular and square free convolutions

Authors
  • Benaych-Georges, Florent
Type
Preprint
Publication Date
Jul 03, 2008
Submission Date
Jul 03, 2008
Source
arXiv
License
Yellow
External links

Abstract

Debbah and Ryan have recently proved a result about the limit empirical singular distribution of the sum of two rectangular random matrices whose dimensions tend to infinity. In this paper, we reformulate it in terms of the rectangular free convolution introduced in a previous paper and then we give a new, shorter, proof of this result under weaker hypothesis: we do not suppose the \pro measure in question in this result to be compactly supported anymore. At last, we discuss the inclusion of this result in the family of relations between rectangular and square random matrices.

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