We prove that for the harmonic measure associated to a random walk on 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.
Ilya Kapovich. Joseph Maher. Catherine Pfaff. Samuel J Taylor. "Random trees in the boundary of outer space." Geom. Topol. 26 (1) 127 - 162, 2022. https://doi.org/10.2140/gt.2022.26.127