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RSA
2008

Simple permutations mix even better

13 years 9 months ago
Simple permutations mix even better
We study the random composition of a small family of O(n3 ) simple permutations on {0, 1}n . Specifically we ask how many randomly selected simple permutations need be composed to yield a permutation that is close to k-wise independent. We improve on the results of Gowers [12] and Hoory et al. [13] and show that up to a polylogarithmic factor, n2 k2 compositions of random permutations from this family suffice. In addition, our results give an explicit construction of a degree O(n3 ) Cayley graph of the alternating group of 2n objects with a spectral gap (2-n /n2 ), which is a substantial improvement over previous constructions.
Alex Brodsky, Shlomo Hoory
Added 28 Dec 2010
Updated 28 Dec 2010
Type Journal
Year 2008
Where RSA
Authors Alex Brodsky, Shlomo Hoory
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