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

Understand

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.