ON THE ALMOST EIGENVECTORS OF RANDOM REGULAR GRAPHS By

@inproceedings{Backhausz2018ONTA,
title={ON THE ALMOST EIGENVECTORS OF RANDOM REGULAR GRAPHS By},
author={{\'A}gnes Backhausz and Bal{\'a}zs Szegedy},
year={2018}
}

Let d ≥ 3 be fixed and G be a large random d-regular graph on n vertices. We show that if n is large enough then the entry distribution of every almost eigenvector of G (with entry sum 0 and normalized to have length √ n) is close to some Gaussian distribution N(0, σ) in the weak topology where 0 ≤ σ ≤ 1. Our theorem holds even in the stronger sense when many entries are looked at simultaneously in small random neighborhoods of the graph. Furthermore, we also get the Gaussianity of the joint… CONTINUE READING