The DOI matches its Crossref record.
Random matrices: Universality of local eigenvalue statistics
Open accessAbstract
In this paper, we consider the universality of the local eigenvalue statistics of random matrices. Our main result shows that these statistics are determined by the first four moments of the distribution of the entries. As a consequence, we derive the universality of eigenvalue gap distribution and k-point correlation, and many other statistics (under some mild assumptions) for both Wigner Hermitian matrices and Wigner real symmetric matrices.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Torquato, S. (2018) · Physics Reports · doi:10.1016/j.physrep.2018.03.001 · Cited by 499
Rigidity of eigenvalues of generalized Wigner matrices
Erdős, L., Yau, H.-T., & Yin, J. (2012) · Advances in Mathematics · doi:10.1016/j.aim.2011.12.010 · Cited by 345
Bulk universality for generalized Wigner matrices
Erdős, L., Yau, H.-T., & Yin, J. (2012) · Probability Theory and Related Fields · doi:10.1007/s00440-011-0390-3 · Cited by 254
Local law and Tracy–Widom limit for sparse random matrices
Lee, J. O., & Schnelli, K. (2018) · Probability Theory and Related Fields · doi:10.1007/s00440-017-0787-8 · Cited by 87
Metadata
- Authors
- Tao, T., & Vu, V.
- Venue
- Acta Mathematica
- Publisher
- International Press of Boston
- Published
- 2011
- Volume
- 206
- Issue
- 1
- Pages
- 127-204
- ISSN
- 0001-5962 (ISSN-L)
- OpenAlex
- W1998731194
- Cited by
- 442
- References
- 0
- FWCI
- 35.61
- Type
- journal article
- Language
- en
- Open access
- diamond
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Random matrices: Universality of local eigenvalue statistics. https://app.cochat.ai/papers/10.1007/s11511-011-0061-3
- The paper
- Tao, T., & Vu, V. (2011). Random matrices: Universality of local eigenvalue statistics. Acta Mathematica. https://doi.org/10.1007/s11511-011-0061-3
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
