Abstract
If A is a nite subset of a free group with at least two noncommuting elements, thenjA A Aj jAj 2 (logjAj)O(1) . More generally, the same conclusion holds in an arbitrary virtually free group, unless A generates a virtually cyclic subgroup. The central part of the proof of this result is carried on by estimating the number of collisions in multiple products A1 ::: Ak. We include a few simple observations showing that in this \statistical context
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