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.Comment: 8 page
