Random trees in the boundary of Outer space

Abstract

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.

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

References in corpus (5)

• The co-surface graph and the geometry of hyperbolic free group extensions
• Reducing systems for very small trees
• Ergodic decompositions for folding and unfolding paths in Outer space
• On the topological dimension of the Gromov boundaries of some hyperbolic $Out(F_N)$-graphs
• Recurrence of quadratic differentials for harmonic measure

Cited by in corpus (1)

• Taking the High-Edge Route Through Outer Space in Rank 3