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Quantitative eigenvector universality for generalized Wigner matrices

  • Lucas Benigni
  • Patrick Lopatto
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Abstract

We present a novel approach to eigenvector universality for generalized Wigner matrices. Our main consequences are asymptotic normality of joint eigenvector projections everywhere in the spectrum as well as, under a uniform subexponential decay assumption, convergence of the extremal process of eigenvector entries and the resulting Gumbel law for the largest entry of an eigenvector. In the case of smooth entries, we are able to obtain joint normality of an explicit growing number of eigenvector projections, and we are also able to obtain explicit rates of convergence in Kolmogorov distance, which are nearly optimal for a fixed number of projections. This is based on a new analysis of the Dyson vector flow which does not rely on the eigenvector moment flow.

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Cite

BibTeXRIS
BibTeX
@misc{benigni2026quantitative,
  title = {{Quantitative eigenvector universality for generalized Wigner matrices}},
  author = {Lucas Benigni and Patrick Lopatto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.06419},
  eprint = {2606.06419},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.06419},
}
RIS
TY  - UNPB
TI  - Quantitative eigenvector universality for generalized Wigner matrices
AU  - Lucas Benigni
AU  - Patrick Lopatto
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2606.06419
UR  - https://arxiv.org/abs/2606.06419
AB  - We present a novel approach to eigenvector universality for generalized Wigner matrices. Our main consequences are asymptotic normality of joint eigenvector projections everywhere in the spectrum as well as, under a uniform subexponential decay assumption, convergence of the extremal process of eigenvector entries and the resulting Gumbel law for the largest entry of an eigenvector. In the case of smooth entries, we are able to obtain joint normality of an explicit growing number of eigenvector projections, and we are also able to obtain explicit rates of convergence in Kolmogorov distance, which are nearly optimal for a fixed number of projections. This is based on a new analysis of the Dyson vector flow which does not rely on the eigenvector moment flow.
ER  -