The Tracy--Widom law for some sparse random matrices
Mathematical Physics
2016-12-20 v6 math.MP
Spectral Theory
Abstract
Consider the random matrix obtained from the adjacency matrix of a random d-regular graph by multiplying every entry by a random sign. The largest eigenvalue converges, after proper scaling, to the Tracy--Widom distribution.
Keywords
Cite
@article{arxiv.0903.4295,
title = {The Tracy--Widom law for some sparse random matrices},
author = {Sasha Sodin},
journal= {arXiv preprint arXiv:0903.4295},
year = {2016}
}
Comments
The proof contains a serious mistake, and Lemma 5 can not be true as stated. For example, the probability that the graph is not connected tends to zero slower than eq. 4 would imply. I am grateful to Charles Bordenave and Sandrine P\'ech\'e who brought this to my attention