Random Cayley Graphs with O(log[G]) Generators Are Expanders

  title={Random Cayley Graphs with O(log[G]) Generators Are Expanders},
  author={Igor Pak},
Let G be a finite group. Choose a set S of sizek uniformly from G and consider a lazy random walk on the corresponding Cayley graph Γ (G,S). We show that for almost all choices of S givenk = 2a log2 |G|, a > 1, we have Reλ1 ≤ 1−1/2a. A similar but weaker result was obtained earlier by Alon and Roichman (see [4]). 

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