- journal article metadata
European Mathematical Society Publishing House
2018-06-03 23:30:01
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
93
2018
2
Random walks and boundaries of CAT(0) cubical complexes
Talia
Fernós
University of North Carolina, Greensboro, USA
Jean
Lécureux
Université Paris-Sud 11, Orsay, France
Frédéric
Mathéus
Université de Bretagne-Sud, Vannes, France
CAT(0) cube complexes, Roller boundary, visual boundary, random walks, stationary measure, drift
We show under weak hypotheses that the pushforward {$Z_no$} of a random-walk to a CAT(0) cube complex converges to a point on the boundary. We introduce the notion of squeezing points, which allows us to consider the convergence in either the Roller boundary or the visual boundary, with the appropriate hypotheses. This study allows us to show that any nonelementary action necessarily contains regular elements, that is, elements that act as rank-1 hyperbolic isometries in each irreducible factor of the essential core.
Group theory and generalizations
Probability theory and stochastic processes
291
333
10.4171/CMH/435
http://www.ems-ph.org/doi/10.4171/CMH/435
5
31
2018