On the largest eigenvalue of a sparse random subgraph of the hypercube

Alexander Soshnikov

On the largest eigenvalue of a sparse random subgraph of the hypercube

Combinatorics 2007-05-23 v1 Mathematical Physics math.MP Probability

Authors: Alexander Soshnikov

Abstract

We consider a sparse random subraph of the $n$ -cube where each edge appears independently with small probability $p(n) =O(n^{-1+o(1)})$ . In the most interesting regime when $p(n)$ is not exponentially small we prove that the largest eigenvalue of the graph is asymtotically equal to the square root of the maximum degree.

Keywords

random graphs spectral graph theory random matrix theory

Cite

@article{arxiv.math/0107229,
  title  = {On the largest eigenvalue of a sparse random subgraph of the hypercube},
  author = {Alexander Soshnikov},
  journal= {arXiv preprint arXiv:math/0107229},
  year   = {2007}
}

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