@article{2697,
  abstract     = {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       = {László Erdös and Knowles, Antti and Yau, Horng-Tzer and Yin, Jun},
  journal      = {Communications in Mathematical Physics},
  number       = {1},
  pages        = {367 -- 416},
  publisher    = {Springer},
  title        = {{Delocalization and diffusion profile for random band matrices}},
  doi          = {10.1007/s00220-013-1773-3},
  volume       = {323},
  year         = {2013},
}