.png){kind=icon}
.png){kind=icon}
Return
Extremal eigenvectors of sparse random matrices
.png){kind=icon}
PRE
AI
H
H
W
DOI：10.1007/s00440-026-01472-2.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We consider a class of sparse random matrices, which includes the adjacency matrix of the Erd & odblac;s-R & eacute;nyi graph G(N,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{G}(N,p)$$\end{document}. For N-1+o(1)<= p <= 1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N<^>{-1+o(1)}\leqslant p\leqslant 1/2$$\end{document}, we show that the non-trivial edge eigenvectors are asymptotically jointly normal. The main ingredient of the proof is an algorithm that directly computes the joint eigenvector distributions, without comparisons with GOE. The method is applicable in general. As an illustration, we also use it to prove the normal fluctuation in quantum ergodicity at the edge for Wigner matrices. Another ingredient of the proof is the isotropic local law for sparse matrices, which at the same time improves several existing results.
Keywords:
EIGENVALUE STATISTICS
SPECTRAL STATISTICS
FLUCTUATIONS
Journal
P
IF:
1.6
Papers:
61
Citations:
0
Organization
Cited Papers