---
_id: '1864'
abstract:
- lang: eng
text: "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"
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Antti
full_name: Knowles, Antti
last_name: Knowles
citation:
ama: 'Erdös L, Knowles A. The Altshuler–Shklovskii formulas for random band matrices
II: The general case. Annales Henri Poincare. 2015;16(3):709-799. doi:10.1007/s00023-014-0333-5'
apa: 'Erdös, L., & Knowles, A. (2015). The Altshuler–Shklovskii formulas for
random band matrices II: The general case. Annales Henri Poincare. Springer.
https://doi.org/10.1007/s00023-014-0333-5'
chicago: 'Erdös, László, and Antti Knowles. “The Altshuler–Shklovskii Formulas for
Random Band Matrices II: The General Case.” Annales Henri Poincare. Springer,
2015. https://doi.org/10.1007/s00023-014-0333-5.'
ieee: 'L. Erdös and A. Knowles, “The Altshuler–Shklovskii formulas for random band
matrices II: The general case,” Annales Henri Poincare, vol. 16, no. 3.
Springer, pp. 709–799, 2015.'
ista: 'Erdös L, Knowles A. 2015. The Altshuler–Shklovskii formulas for random band
matrices II: The general case. Annales Henri Poincare. 16(3), 709–799.'
mla: 'Erdös, László, and Antti Knowles. “The Altshuler–Shklovskii Formulas for Random
Band Matrices II: The General Case.” Annales Henri Poincare, vol. 16, no.
3, Springer, 2015, pp. 709–99, doi:10.1007/s00023-014-0333-5.'
short: L. Erdös, A. Knowles, Annales Henri Poincare 16 (2015) 709–799.
date_created: 2018-12-11T11:54:26Z
date_published: 2015-03-01T00:00:00Z
date_updated: 2021-01-12T06:53:42Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s00023-014-0333-5
ec_funded: 1
intvolume: ' 16'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1309.5107
month: '03'
oa: 1
oa_version: Preprint
page: 709 - 799
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annales Henri Poincare
publication_status: published
publisher: Springer
publist_id: '5233'
scopus_import: 1
status: public
title: 'The Altshuler–Shklovskii formulas for random band matrices II: The general
case'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16
year: '2015'
...