Abstract
We investigate eigenvector statistics of the Truncated Unitary ensemble in the weakly non-unitary case , that is when only one row and column are removed. We provide an explicit description of generalized overlaps as deterministic functions of the eigenvalues, as well as a method to derive an exact formula for the expectation of diagonal overlaps (or squared eigenvalue condition numbers), conditionally on one eigenvalue. This complements recent results obtained in the opposite regime when , suggesting possible extensions to for all values of M.
Funding Statement
The author gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.
Acknowledgments
The author’s gratitude goes to Jana Reker as well as to the anonymous referee for their careful proofreading and comments.
Citation
Guillaume Dubach. "Explicit formulas concerning eigenvectors of weakly non-unitary matrices." Electron. Commun. Probab. 28 1 - 11, 2023. https://doi.org/10.1214/22-ECP507
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