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Cited by 254

The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.

Bulk universality for generalized Wigner matrices

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Erdős, László, Yau, Horng-Tzer, Yin, Jun·2012·Probability Theory and Related Fields
DOI 10.1007/s00440-011-0390-3
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Abstract

Consider N × N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure νij with a subexponential decay. Let $${\sigma_{ij}^2}$$ be the variance for the probability measure νij with the normalization property that $${\sum_{i} \sigma^2_{ij} = 1}$$ for all j. Under essentially the only condition that $${c\le N \sigma_{ij}^2 \le c^{-1}}$$ for some constant c > 0, we prove that, in the limit N → ∞, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth M the local semicircle law holds to the energy scale M−1.

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Metadata

Authors
Erdős, L., Yau, H.-T., & Yin, J.
Venue
Probability Theory and Related Fields
Publisher
Springer Science and Business Media LLC
Published
2011-10-06
Volume
154
Issue
1-2
Pages
341-407
ISSN
  • 0178-8051 (ISSN-L)
  • 1432-2064
DOI
10.1007/s00440-011-0390-3
OpenAlex
W2070535307
Cited by
254
References
13
FWCI
19.20
Type
journal article
Language
en
Open access
bronze

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CoChat. (2026). Citation check: Bulk universality for generalized Wigner matrices. https://app.cochat.ai/papers/10.1007/s00440-011-0390-3
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Erdős, L., Yau, H.-T., & Yin, J. (2012). Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-011-0390-3

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