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The Non-Commutative Cycle Lemma

arXiv:0903.4601 · doi:10.1016/j.jcta.2009.12.002

Abstract

We present a non-commutative version of the cycle lemma of Dvoretsky and Motzkin that applies to free groups and use this result to solve a number of problems involving cyclic reduction in the free group. We also describe an application to random matrices, in particular the fluctuations of Kesten's Law.

13 pages, minor corrections and improvements