Some estimates for generalized Wigner matrix linear spectral statistics

Benjamin Landon

Some estimates for generalized Wigner matrix linear spectral statistics

Probability 2024-12-19 v1

Authors: Benjamin Landon

Abstract

We consider the characteristic function of linear spectral statistics of generalized Wigner matrices. We provide an expansion of the characteristic function with error $\mathcal{O} ( N^{-1})$ around its limiting Gaussian form, and identify sub-leading non-Gaussian corrections of size $\mathcal{O} (N^{-1/2})$ . Prior expansions with this error rate held only for Wigner matrices; only a weaker error rate was available for more general matrix ensembles. We provide some applications.

Keywords

random matrix theory gaussian processes spectral theory

Cite

@article{arxiv.2412.14070,
  title  = {Some estimates for generalized Wigner matrix linear spectral statistics},
  author = {Benjamin Landon},
  journal= {arXiv preprint arXiv:2412.14070},
  year   = {2024}
}

Comments

82 pages, preliminary version. Extends part of arXiv:2204.03419. That article will be revised

Some estimates for generalized Wigner matrix linear spectral statistics

Abstract

Keywords

Cite

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