---
res:
bibo_abstract:
- We consider quadratic forms of deterministic matrices A evaluated at the random
eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the
columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as
long as the deterministic matrix has rank much smaller than √N, the distributions
of the extrema of these quadratic forms are asymptotically the same as if the
eigenvectors were independent Gaussians. This reduces the problem to Gaussian
computations, which we carry out in several cases to illustrate our result, finding
Gumbel or Weibull limiting distributions depending on the signature of A. Our
result also naturally applies to the eigenvectors of any invariant ensemble.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: László
foaf_name: Erdös, László
foaf_surname: Erdös
foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-5366-9603
- foaf_Person:
foaf_givenName: Benjamin
foaf_name: McKenna, Benjamin
foaf_surname: McKenna
foaf_workInfoHomepage: http://www.librecat.org/personId=b0cc634c-d549-11ee-96c8-87338c7ad808
orcid: 0000-0003-2625-495X
bibo_doi: 10.1214/23-AAP2000
bibo_issue: 1B
bibo_volume: 34
dct_date: 2024^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1050-5164
dct_language: eng
dct_publisher: Institute of Mathematical Statistics@
dct_title: Extremal statistics of quadratic forms of GOE/GUE eigenvectors@
...