Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 4 min ago
PreprintCC BY 4.0arXiv

Beyond normal fluctuations in local laws for Wigner matrices

  • László Erdős
  • Oleksii Kolupaiev
Open at sourcePDFDOICite

Abstract

We identify non-Gaussian corrections to the central limit theorem for the global and local laws, i.e. for Stieltjes transform of the empirical eigenvalue distribution of a large real symmetric or complex Hermitian Wigner matrix. We find that in the real case the rate of convergence in this CLT is substantially slower than in the complex case. For the proofs, we develop new static and dynamic hierarchies of extended cumulants up to any order that can be analyzed by a refinement of the zigzag strategy.

Related

  1. Eigenstate thermalisation at the edge for Wigner matrices
    Giorgio Cipolloni, László Erdős, Joscha Henheik
    Annales de l Institut Henri Poincaré Probabilités et StatistiquesPeer-reviewedLicence not statedFull text33 citedStatisticsOpenAlex
  2. Precise Delocalisation and Gumbel Laws for Eigenvectors of Wigner Matrices
    Mohammed Osman
    arXivPreprintarXiv licenceFull textMathematical physicsProbabilityarXiv
  3. Infinitesimal Freeness of Wigner Matrices
    Samuel Gurrola-Viramontes, James A. Mingo
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Quantitative eigenvector universality for generalized Wigner matrices
    Lucas Benigni, Patrick Lopatto
    arXivPreprintarXiv licenceFull textMathematical physicsProbabilityarXiv
  5. Quantum Fluctuations and Wigner Dynamics of a Carbon Nanotube Oscillator Driven by an Atomic Force Microscope
    Conrad Silio, Cristian Staii
    arXivPreprintCC BY-NC-SA 4.0Full textMathematical physicsCondensed matterarXiv

Cite

BibTeXRIS
BibTeX
@misc{erdos2026beyond,
  title = {{Beyond normal fluctuations in local laws for Wigner matrices}},
  author = {László Erdős and Oleksii Kolupaiev},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03924},
  eprint = {2609.03924},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03924},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Beyond normal fluctuations in local laws for Wigner matrices
AU  - László Erdős
AU  - Oleksii Kolupaiev
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03924
UR  - https://arxiv.org/abs/2609.03924
AB  - We identify non-Gaussian corrections to the central limit theorem for the global and local laws, i.e. for Stieltjes transform of the empirical eigenvalue distribution of a large real symmetric or complex Hermitian Wigner matrix. We find that in the real case the rate of convergence in this CLT is substantially slower than in the complex case. For the proofs, we develop new static and dynamic hierarchies of extended cumulants up to any order that can be analyzed by a refinement of the zigzag strategy.
ER  -