---
res:
bibo_abstract:
- "The Altshuler–Shklovskii formulas (Altshuler and Shklovskii, BZh Eksp Teor Fiz
91:200, 1986) predict, for any disordered quantum system in the diffusive regime,
a universal power law behaviour for the correlation functions of the mesoscopic
eigenvalue density. In this paper and its companion (Erdős and Knowles, The Altshuler–Shklovskii
formulas for random band matrices I: the unimodular case, 2013), we prove these
formulas for random band matrices. In (Erdős and Knowles, The Altshuler–Shklovskii
formulas for random band matrices I: the unimodular case, 2013) we introduced
a diagrammatic approach and presented robust estimates on general diagrams under
certain simplifying assumptions. In this paper, we remove these assumptions by
giving a general estimate of the subleading diagrams. We also give a precise analysis
of the leading diagrams which give rise to the Altschuler–Shklovskii power laws.
Moreover, we introduce a family of general random band matrices which interpolates
between real symmetric (β = 1) and complex Hermitian (β = 2) models, and track
the transition for the mesoscopic density–density correlation. Finally, we address
the higher-order correlation functions by proving that they behave asymptotically
according to a Gaussian process whose covariance is given by the Altshuler–Shklovskii
formulas.\r\n@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: Antti
foaf_name: Knowles, Antti
foaf_surname: Knowles
bibo_doi: 10.1007/s00023-014-0333-5
bibo_issue: '3'
bibo_volume: 16
dct_date: 2015^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: 'The Altshuler–Shklovskii formulas for random band matrices II: The general
case@'
...