Edge statistics for singular values of products of rectangular complex Ginibre matrices (2507.07431v1)

Published 10 Jul 2025 in math.PR

Abstract: We investigate the edge statistics of singular values for products of independent rectangular complex Ginibre matrices. Building on work \cite{LWW23}, which introduced the depth-to-width ratio (DWR) and established the critical kernel, we show that the DWR acts as a sharp threshold: local statistics exhibit Gaussian fluctuations in the low-DWR regime, while the Airy kernel emerges at the soft edge in the high-DWR regime.

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Authors (1)

Yandong Gu

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