On the Largest Eigenvalue of a Random Subgraph of the Hypercube
Probability
2009-11-07 v2 Combinatorics
Abstract
Let G be a random subgraph of the n-cube where each edge appears randomly and independently with probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely \lambda_1(G)= (1+o(1)) max(\Delta^{1/2}(G),np), where \Delta(G) is the maximum degree of G and o(1) term tends to zero as max (\Delta^{1/2}(G), np) tends to infinity.
Cite
@article{arxiv.math/0209178,
title = {On the Largest Eigenvalue of a Random Subgraph of the Hypercube},
author = {Alexander Soshnikov and Benny Sudakov},
journal= {arXiv preprint arXiv:math/0209178},
year = {2009}
}
Comments
Final version (to appear in Commun. Math. Phys.)