Local Statistics of Singular Values for Products of Truncated Unitary Matrices
Abstract
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 matricesABK19LWW23, the current work provides the complete characterization in the truncated unitary matrix setting.
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