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

@inproceedings{Pak1999RandomCG, title={Random Cayley Graphs with O(log[G]) Generators Are Expanders}, author={Igor Pak}, booktitle={ESA}, year={1999} }

- Published 1999 in ESA
DOI:10.1007/3-540-48481-7_45

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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## Erdos-Renyi Sequences and Deterministic construction of Expanding Cayley Graphs

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#### References

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Showing 1-10 of 12 references

## Roichman : On random random walks

## Fill:Reversible Markov Chains and Random Walks on Graphs monograph in preparation

## Hall : Probabilistic methods in group theory

## Random random walks on Z d 2 , Prob

## Roichman:Random Cayley graphs and expanders

View 2 Excerpts

## Representations in Probability and Statistics

## Diaconis: Strong uniform times and finite random walks

View 1 Excerpt

## Diaconis: Shuffling cards and stopping times

View 1 Excerpt