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Random trees in the
boundary of outer space
Ilya Kapovich, Joseph Maher, Catherine Pfaff and Samuel J Taylor |
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Geometry & Topology 26 (2022) 127–162
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DOI: 10.2140/gt.2022.26.127
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Abstract |
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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. |
Keywords
free group, random walk, outer space, free group
automorphisms, train track maps
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Mathematical Subject Classification
Primary: 20F65
Secondary: 37D99, 57M99
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References |
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
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Authors |
| Ilya Kapovich | |
| Department of Mathematics and
Statistics Hunter College of CUNY New York, NY United States |
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| http://math.hunter.cuny.edu/ilyakapo/ | |
| Joseph Maher | |
| Department of Mathematics CUNY College of Staten Island and CUNY Graduate Center Staten Island, NY United States |
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| http://www.math.csi.cuny.edu/~maher/ | |
| Catherine Pfaff | |
| Department of Mathematics and
Statistics Queen’s University Kingston, ON Canada |
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| https://mast.queensu.ca/~cpfaff/ | |
| Samuel J Taylor | |
| Department of Mathematics Temple University Philadelphia, PA United States |
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| https://math.temple.edu/~samuel.taylor/ | |
