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This article is available for purchase or by subscription. See below.
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 result answers a question of Mladen
Bestvina.
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Keywords
free group, random walk, outer space, free group
automorphisms, train track maps
Mathematical Subject Classification
Primary: 20F65
Secondary: 37D99, 57M99
Publication
Received: 5 May 2019
Revised: 31 January 2021
Accepted: 28 February 2021
Published: 5 April 2022
Proposed: Walter Neumann
Seconded: Mladen Bestvina, Dmitri Burago