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arXiv · 2508.05802

Localization of One-Dimensional Random Band Matrices

Reuben Drogin
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Abstract

We consider a general class of $n\times n$ random band matrices with bandwidth $W$. When $W^2\ll n$, we prove that with high probability the eigenvectors of such matrices are localized and decay exponentially at the sharp scale $W^2$. Combined with the delocalization results of Yau and Yin [arXiv:2501.01718] and of Erd\H{o}s and Riabov [arXiv:2506.06441], this establishes the conjectured localization-delocalization transition for a large class of random band matrices.

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Reuben Drogin. 2025-08-07. Localization of One-Dimensional Random Band Matrices. https://arxiv.org/abs/2508.05802

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