Universality for a class of random band matrices

Paul Bourgade New York University, Courant Institute Laszlo Erdos Institute of Science and Technology Austria Horng-Tzer Yau Harvard University Jun Yin University of Wisconsin, Madison

Probability mathscidoc:1608.28002

2016
We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, $W \sim N$. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.
random band matrices, quantum unique ergodicity
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@inproceedings{paul2016universality,
  title={Universality for a class of random band matrices},
  author={Paul Bourgade, Laszlo Erdos, Horng-Tzer Yau, and Jun Yin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160823001621117919391},
  year={2016},
}
Paul Bourgade, Laszlo Erdos, Horng-Tzer Yau, and Jun Yin. Universality for a class of random band matrices. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160823001621117919391.
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