Global and local limits for products of rectangular Ginibre matrices

Published 20 Oct 2025 in math.PR | (2510.17282v1)

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.

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Global spectral density for products with heterogeneous rectangularity parameters

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Yandong Gu

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