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arXiv · 2212.14638

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

Guillaume Dubach·Jana Reker
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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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Guillaume Dubach, Jana Reker. 2022-12-30. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. https://doi.org/10.1142/s2010326324500072

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