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1 February 2016 The Poisson boundary of Out(FN)
Camille Horbez
Duke Math. J. 165(2): 341-369 (1 February 2016). DOI: 10.1215/00127094-3166308

Abstract

Let μ be a probability measure on Out(FN) with finite first logarithmic moment with respect to the word metric, finite entropy, and whose support generates a nonelementary subgroup of Out(FN). We show that almost every sample path of the random walk on (Out(FN),μ), when realized in Culler and Vogtmann’s outer space, converges to the simplex of a free, arational tree. We then prove that the space FI of simplices of free and arational trees, equipped with the hitting measure, is the Poisson boundary of (Out(FN),μ). Using Bestvina and Reynolds’s and Hamenstädt’s description of the Gromov boundary of the complex FFN of free factors of FN, this gives a new proof of the fact, due to Calegari and Maher, that the realization in FFN of almost every sample path of the random walk converges to a boundary point. We get in addition that FFN, equipped with the hitting measure, is the Poisson boundary of (Out(FN),μ).

Citation

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Camille Horbez. "The Poisson boundary of Out(FN)." Duke Math. J. 165 (2) 341 - 369, 1 February 2016. https://doi.org/10.1215/00127094-3166308

Information

Received: 27 June 2014; Revised: 1 March 2015; Published: 1 February 2016
First available in Project Euclid: 19 January 2016

zbMATH: 06556670
MathSciNet: MR3457676
Digital Object Identifier: 10.1215/00127094-3166308

Subjects:
Primary: 20F65
Secondary: 60B15

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 2 • 1 February 2016
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