Local Statistics of Singular Values for Products of Truncated Unitary Matrices

Fuente: arXiv
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Main Authors: Gu, Yandong, Liu, Dang-Zheng
Format: Preprint
Published: 2025
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author Gu, Yandong
Liu, Dang-Zheng
author_facet Gu, Yandong
Liu, Dang-Zheng
contents This paper investigates local spectral statistics of singular values for many products of independent large rectangular matrices, sampled from the ensemble of truncated unitary matrices with the invariant Haar measure. Our main contribution establishes a universal three-phase transition in these statistics, demonstrating an interpolation beween GUE statistics and classical Gaussian behavior. While such transition was previously known for products of complex Gaussian matrices\cite{ABK19}\cite{LWW23}, the current work provides the complete characterization in the truncated unitary matrix setting.
format Preprint
id arxiv_https___arxiv_org_abs_2506_14193
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Local Statistics of Singular Values for Products of Truncated Unitary Matrices
Gu, Yandong
Liu, Dang-Zheng
Probability
60B20
This paper investigates local spectral statistics of singular values for many products of independent large rectangular matrices, sampled from the ensemble of truncated unitary matrices with the invariant Haar measure. Our main contribution establishes a universal three-phase transition in these statistics, demonstrating an interpolation beween GUE statistics and classical Gaussian behavior. While such transition was previously known for products of complex Gaussian matrices\cite{ABK19}\cite{LWW23}, the current work provides the complete characterization in the truncated unitary matrix setting.
title Local Statistics of Singular Values for Products of Truncated Unitary Matrices
topic Probability
60B20
url https://arxiv.org/abs/2506.14193