Work

Local Law and Eigenvector Delocalization for Random Lifts

Year: 2026

Type: preprint

Abstract: We establish a quantitative local law for random $N$-lifts of a fixed finite connected simple graph with minimum degree at least three. Away from the singular energies of the universal-cover spectrum, we obtain high-probability entrywise Green's function estimates down to spectral scales $(\log N)^C/N$, uniformly in the bulk and near regular edges and cusps. As a consequence, we establish complete eigenvector delocalization: every normalized eigenvector $u$ whose eigenvalue stays a small but fixed positive distance away from the singular energies satisfies $\|u\|_\infty\leq(\log N)^C/\sqrt{N}$ with high probability.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.37463

Authors: Huang, Jiaoyang, Xu, Ruizhe

Institutions: Courant Institute of Mathematical Sciences, New York University, University of Hong Kong

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of Pennsylvania

Awards: Random Matrices, Random Graphs, and Deep Neural Networks, Dynamical and Spatial Asymptotics of Large Disordered Systems

OpenAlex ID: W7224102136

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