The Non-Commutative Cycle Lemma
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math.OA
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cyclefreelemmanon-commutativeapplicationappliescyclicdescribe
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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.
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