Edge statistics for singular values of products of rectangular complex Ginibre matrices
Probability
2025-07-11 v1
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.
Cite
@article{arxiv.2507.07431,
title = {Edge statistics for singular values of products of rectangular complex Ginibre matrices},
author = {Yandong Gu},
journal= {arXiv preprint arXiv:2507.07431},
year = {2025}
}
Comments
11 pages,2 figures