Dynamics of a rank-one multiplicative perturbation of a unitary matrix

2022/12/30 by Guillaume Dubach, Dubach, Guillaume, Jana Reker +1 · 1 citation
Mathematics · #15B52 (Primary) 47B93 (Secondary) #60B20 #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2212.14638

openalex publication_date 2022/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on U that hold for a variety of unitary random matrix models.

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• Zeros Of Random Analytic Functions And Spectral Properties Of Perturbed Unitary Matrices

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