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

- Author(s): Soshnikov, Alexander
- et al.

## Published Web Location

https://arxiv.org/pdf/math/0107229.pdfNo data is associated with this publication.

## 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.