English

Random trees in the boundary of Outer space

Geometric Topology 2022-04-20 v3 Group Theory

Abstract

We prove that for the harmonic measure associated to a random walk on Out(Fr)(F_r) satisfying some mild conditions, a typical tree in the boundary of Outer space is trivalent and nongeometric. This answers a question of M. Bestvina.

Keywords

Cite

@article{arxiv.1904.10026,
  title  = {Random trees in the boundary of Outer space},
  author = {Ilya Kapovich and Joseph Maher and Catherine Pfaff and Samuel J. Taylor},
  journal= {arXiv preprint arXiv:1904.10026},
  year   = {2022}
}

Comments

28 pages; minor typesetting issues corrected from the previous update. Accepted for publication in Geometry & Topology

R2 v1 2026-06-23T08:46:40.651Z