---
_id: '2697'
abstract:
- lang: eng
  text: We consider Hermitian and symmetric random band matrices H = (h xy ) in d⩾1
    d ⩾ 1 dimensions. The matrix entries h xy , indexed by x,y∈(Z/LZ)d x , y ∈ ( Z
    / L Z ) d , are independent, centred random variables with variances sxy=E|hxy|2
    s x y = E | h x y | 2 . We assume that s xy is negligible if |x − y| exceeds the
    band width W. In one dimension we prove that the eigenvectors of H are delocalized
    if W≫L4/5 W ≫ L 4 / 5 . We also show that the magnitude of the matrix entries
    |Gxy|2 | G x y | 2 of the resolvent G=G(z)=(H−z)−1 G = G ( z ) = ( H - z ) - 1
    is self-averaging and we compute E|Gxy|2 E | G x y | 2 . We show that, as L→∞
    L → ∞ and W≫L4/5 W ≫ L 4 / 5 , the behaviour of E|Gxy|2 E | G x y | 2 is governed
    by a diffusion operator whose diffusion constant we compute. Similar results are
    obtained in higher dimensions.
author:
- first_name: László
  full_name: László Erdös
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Antti
  full_name: Knowles, Antti
  last_name: Knowles
- first_name: Horng
  full_name: Yau, Horng-Tzer
  last_name: Yau
- first_name: Jun
  full_name: Yin, Jun
  last_name: Yin
citation:
  ama: Erdös L, Knowles A, Yau H, Yin J. Delocalization and diffusion profile for
    random band matrices. <i>Communications in Mathematical Physics</i>. 2013;323(1):367-416.
    doi:<a href="https://doi.org/10.1007/s00220-013-1773-3">10.1007/s00220-013-1773-3</a>
  apa: Erdös, L., Knowles, A., Yau, H., &#38; Yin, J. (2013). Delocalization and diffusion
    profile for random band matrices. <i>Communications in Mathematical Physics</i>.
    Springer. <a href="https://doi.org/10.1007/s00220-013-1773-3">https://doi.org/10.1007/s00220-013-1773-3</a>
  chicago: Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “Delocalization and
    Diffusion Profile for Random Band Matrices.” <i>Communications in Mathematical
    Physics</i>. Springer, 2013. <a href="https://doi.org/10.1007/s00220-013-1773-3">https://doi.org/10.1007/s00220-013-1773-3</a>.
  ieee: L. Erdös, A. Knowles, H. Yau, and J. Yin, “Delocalization and diffusion profile
    for random band matrices,” <i>Communications in Mathematical Physics</i>, vol.
    323, no. 1. Springer, pp. 367–416, 2013.
  ista: Erdös L, Knowles A, Yau H, Yin J. 2013. Delocalization and diffusion profile
    for random band matrices. Communications in Mathematical Physics. 323(1), 367–416.
  mla: Erdös, László, et al. “Delocalization and Diffusion Profile for Random Band
    Matrices.” <i>Communications in Mathematical Physics</i>, vol. 323, no. 1, Springer,
    2013, pp. 367–416, doi:<a href="https://doi.org/10.1007/s00220-013-1773-3">10.1007/s00220-013-1773-3</a>.
  short: L. Erdös, A. Knowles, H. Yau, J. Yin, Communications in Mathematical Physics
    323 (2013) 367–416.
date_created: 2018-12-11T11:59:07Z
date_published: 2013-10-01T00:00:00Z
date_updated: 2021-01-12T06:59:07Z
day: '01'
doi: 10.1007/s00220-013-1773-3
extern: 1
intvolume: '       323'
issue: '1'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1205.5669
month: '10'
oa: 1
page: 367 - 416
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4199'
quality_controlled: 0
status: public
title: Delocalization and diffusion profile for random band matrices
type: journal_article
volume: 323
year: '2013'
...