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

组合数学 2007-05-23 v1 数学物理 math.MP 概率论

作者: Alexander Soshnikov

摘要

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.

关键词

random graphs spectral graph theory random matrix theory

引用

@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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