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

Abstract

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.

arXiv commentCorrected references and typos

References in corpus (2)

• Sharp Bounds for Sums Associated to Graphs of Matrices
• Spectral norm of products of random and deterministic matrices

Cited by in corpus (5)

• On the Asymptotic Spectrum of Products of Independent Random Matrices
• Limit distributions of random matrices
• Asymptotic Spectra of Matrix-Valued Functions of Independent Random Matrices and Free Probability
• Limiting Spectral Distributions of Sums of Products of Non-Hermitian Random Matrices
• Noncrossing partition flow and random matrix models