---
res:
  bibo_abstract:
  - We prove that a very general class of $N\times N$ Hermitian random band matrices
    is in the delocalized phase when the band width $W$ exceeds the critical threshold,
    $W\gg \sqrt{N}$. In this regime, we show that, in the bulk spectrum, the eigenfunctions
    are fully delocalized, the eigenvalues follow the universal Wigner-Dyson statistics,
    and quantum unique ergodicity holds for general diagonal observables with an optimal
    convergence rate. Our results are valid for general variance profiles, arbitrary
    single entry distributions, in both real-symmetric and complex-Hermitian symmetry
    classes. In particular, our work substantially generalizes the recent breakthrough
    result of Yau and Yin [arXiv:2501.01718], obtained for a specific complex Hermitian
    Gaussian block band matrix. The main technical input is the optimal multi-resolvent
    local laws -- both in the averaged and fully isotropic form. We also generalize
    the $\sqrtη$-rule from [arXiv:2012.13215] to exploit the additional effect of
    traceless observables. Our analysis is based on the zigzag strategy, complemented
    with a new global-scale estimate derived using the static version of the master
    inequalities, while the zig-step and the a priori estimates on the deterministic
    approximations are proven dynamically.@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: Volodymyr
      foaf_name: Riabov, Volodymyr
      foaf_surname: Riabov
      foaf_workInfoHomepage: http://www.librecat.org/personId=1949f904-edfb-11eb-afb5-e2dfddabb93b
  bibo_doi: 10.48550/ARXIV.2506.06441
  dct_date: 2025^xs_gYear
  dct_language: eng
  dct_title: The zigzag strategy for random band matrices@
...