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Dynamical Localization for Random Band Matrices up to $W\ll N^{1/4}$

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arxiv 2206.05545 v2 pith:SQHIKMTN submitted 2022-06-11 math-ph math.MPmath.PR

Giorgio Cipolloni , Ron Peled , Jeffrey Schenker , Jacob Shapiro This is my paper · ORCID
classification math-phmath.MPmath.PR
keywords banddynamicallocalizationmatricesrandomadaptiveandersonclass
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abstract

We prove that a large class of $N\times N$ Gaussian random band matrices with band width $W$ exhibits dynamical Anderson localization at all energies when $W \ll N^{1/4}$. The proof uses the fractional moment method and an adaptive Mermin--Wagner style shift.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Delocalization of One-Dimensional Random Band Matrices

    math.PR 2025-01 conditional novelty 8.0 of 10

    For one-dimensional block band matrices with W > N^{1/2+c}, the paper proves the local semicircle law, eigenvector delocalization, quantum unique ergodicity, and GUE universality.

  2. Delocalization of random band matrices at the edge

    math.PR 2025-05 conditional novelty 7.0 of 10

    For random band matrices in dimensions 1 and 2, eigenvectors with energies 2-|E| >> N^{-c} are delocalized, and all eigenvectors are delocalized when the band width exceeds N^{1-d/6}.

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