#### Volume 26, issue 1 (2022)

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Random trees in the boundary of outer space

### Ilya Kapovich, Joseph Maher, Catherine Pfaff and Samuel J Taylor

Geometry & Topology 26 (2022) 127–162
DOI: 10.2140/gt.2022.26.127
##### Abstract

We prove that for the harmonic measure associated to a random walk on $\mathrm{Out}\left({F}_{r}\right)$ satisfying some mild conditions, a typical tree in the boundary of Outer space is trivalent and nongeometric. This result answers a question of Mladen Bestvina.

##### Keywords
free group, random walk, outer space, free group automorphisms, train track maps
##### Mathematical Subject Classification
Primary: 20F65
Secondary: 37D99, 57M99