Random trees in the boundary of Outer space
- Resource Type
- Working Paper
- Authors
- Kapovich, Ilya; Maher, Joseph; Pfaff, Catherine; Taylor, Samuel J.
- Source
- Geom. Topol. 26 (2022) 127-162
- Subject
- Mathematics - Geometric Topology
Mathematics - Group Theory
20F65 (Primary), 57M, 37B, 37D (Secondary)
- Language
We prove that for the harmonic measure associated to a random walk on Out$(F_r)$ satisfying some mild conditions, a typical tree in the boundary of Outer space is trivalent and nongeometric. This answers a question of M. Bestvina.
Comment: 28 pages; minor typesetting issues corrected from the previous update. Accepted for publication in Geometry & Topology