English

Random walks on the mapping class group

Geometric Topology 2019-12-19 v4 Group Theory

Abstract

We show that a random walk on the mapping class group of an orientable surface gives rise to a pseudo-Anosov element with asymptotic probability one. Our methods apply to many subgroups of the mapping class group, including the Torelli group.

Keywords

Cite

@article{arxiv.math/0604433,
  title  = {Random walks on the mapping class group},
  author = {Joseph Maher},
  journal= {arXiv preprint arXiv:math/0604433},
  year   = {2019}
}

Comments

31 pages, 7 figures. v2: Added references to work of Rivin and I. Kapovich. v3: This version now only contains the mapping class group results. The original application to 3-manifolds contained a gap, which is fixed in arXiv:0809.4881. v4: revised version