The Non-Commutative Cycle Lemma

  • Authors:

  • Craig Armstrong;James A. Mingo;Roland Speicher;Jennifer C. H. Wilson

  • Affiliations:

  • Queen's University, Department of Mathematics and Statistics, Jeffery Hall, Kingston, ON K7L 3N6, Canada;Queen's University, Department of Mathematics and Statistics, Jeffery Hall, Kingston, ON K7L 3N6, Canada;Queen's University, Department of Mathematics and Statistics, Jeffery Hall, Kingston, ON K7L 3N6, Canada;Queen's University, Department of Mathematics and Statistics, Jeffery Hall, Kingston, ON K7L 3N6, Canada

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2010

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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.