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

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.

21 pages, 2 figures. Corrected some typos in previous version

References in corpus (3)

• Explicit formulas concerning eigenvectors of weakly non-unitary matrices
• Extreme eigenvalues and the emerging outlier in rank-one non-Hermitian deformations of the Gaussian Unitary Ensemble
• Dynamics of a rank-one perturbation of a Hermitian matrix