# Random trees in the boundary of Outer space

## TL;DR

This paper demonstrates that under certain conditions, a typical tree in the boundary of Outer space, associated with a random walk on Out$(F_r)$, is both trivalent and nongeometric, addressing a question posed by M. Bestvina.

## Contribution

It establishes that harmonic measure on the boundary of Outer space concentrates on trees that are trivalent and nongeometric, providing new insights into the boundary structure.

## Key findings

- Typical trees are trivalent and nongeometric
- Harmonic measure concentrates on these trees
- Addresses a question by M. Bestvina

## 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.