On the asymptotic distribution of singular values of products of large rectangular random matrices

Details On the asymptotic distribution of singular values of products of large rectangular random matrices On the asymptotic distribution of singular values of products of large rectangular random matrices

2010-12-12

arxiv.org/abs/1012.2586v2

Mathematics

Probability

Corrected references and typos

Scientific paper

We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is described by its Stieltjes transform, which satisfies some algebraic equation. In the particular case of square matrices we get a well-known distribution which moments are Fuss-Catalan numbers.

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