Global and local limits for products of rectangular Ginibre matrices

TL;DR

This paper analyzes the singular value distribution of products of independent rectangular Ginibre matrices, deriving the limiting spectral density and demonstrating universal local statistics in the bulk.

Contribution

It extends classical results for square matrices to rectangular matrices, providing new insights into their spectral behavior in the asymptotic limit.

Findings

Limiting spectral density derived for rectangular Ginibre matrix products

Bulk local statistics follow the universal sine kernel

Generalization from square to rectangular matrix products

Abstract

We investigate singular value statistics for products of independent rectangular complex Ginibre matrices. When the rectangularity parameters of the matrices converge to a common limit in the asymptotic regime, the limiting spectral density is derived, and the local statistics in the bulk are shown to be governed by the universal sine kernel. This generalizes the classical results for products of square Ginibre matrices to a specific class of rectangular matrix products.