English

The Non-Commutative Cycle Lemma

Combinatorics 2012-10-25 v2 Operator Algebras

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.

Keywords

Cite

@article{arxiv.0903.4601,
  title  = {The Non-Commutative Cycle Lemma},
  author = {Craig Armstrong and James A. Mingo and Roland Speicher and Jennifer C. H. Wilson},
  journal= {arXiv preprint arXiv:0903.4601},
  year   = {2012}
}

Comments

13 pages, minor corrections and improvements

R2 v1 2026-06-21T12:44:52.336Z