Random trees in the boundary of outer space

Ilya Kapovich; Joseph Maher; Catherine Pfaff; Samuel J Taylor

doi:10.2140/gt.2022.26.127

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2022 Random trees in the boundary of outer space

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

Abstract

We prove that for the harmonic measure associated to a random walk on ${\rm{Out}}({F_r})$ 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.

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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

Information

Received: 5 May 2019; Revised: 31 January 2021; Accepted: 28 February 2021; Published: 2022

First available in Project Euclid: 9 May 2022

Digital Object Identifier: 10.2140/gt.2022.26.127

Subjects:

Primary: 20F65

Secondary: 37D99 , 57M99

Keywords: free group , free group automorphisms , Outer space , Random walk , train track maps

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