---
res:
bibo_abstract:
- We prove a new central limit theorem (CLT) for the difference of linear eigenvalue
statistics of a Wigner random matrix H and its minor H and find that the fluctuation
is much smaller than the fluctuations of the individual linear statistics, as
a consequence of the strong correlation between the eigenvalues of H and H. In
particular, our theorem identifies the fluctuation of Kerov's rectangular Young
diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic
shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel
measure follow the same limiting shape. For this, algebraically motivated, ensemble
a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar
to our result but the variance is different, indicating that the analogy between
the two models has its limitations. Moreover, our theorem shows that Borodin's
result [7] on the convergence of the spectral distribution of Wigner matrices
to a Gaussian free field also holds in derivative sense.@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: Dominik J
foaf_name: Schröder, Dominik J
foaf_surname: Schröder
foaf_workInfoHomepage: http://www.librecat.org/personId=408ED176-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.1093/imrn/rnw330
bibo_issue: '10'
bibo_volume: 2018
dct_date: 2018^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/10737928
dct_language: eng
dct_publisher: Oxford University Press@
dct_title: Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues@
...