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


We show under weak hypotheses that the pushforward {} 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.

Cite this article

Talia Fernós, Jean Lécureux, Frédéric Mathéus, Random walks and boundaries of CAT(0) cubical complexes. Comment. Math. Helv. 93 (2018), no. 2, pp. 291–333

DOI 10.4171/CMH/435