Random walks and boundaries of CAT(0) cubical complexes

DOI10.4171/CMH/435zbMath1494.20059arXiv1609.02577MaRDI QIDQ1645342

Talia Fernós, Frédéric Mathéus, Jean Lécureux

Publication date: 28 June 2018

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.02577

zbMATH Keywords

random walksstationary measuredriftvisual boundaryCAT(0) cube complexesRoller boundary

Mathematics Subject Classification ID

Geometric group theory (20F65) Hyperbolic groups and nonpositively curved groups (20F67) Boundary theory for Markov processes (60J50) Probabilistic methods in group theory (20P05)

Related Items (16)

Measure equivalence classification of transvection-free right-angled Artin groups ⋮ Cocycle superrigidity from higher rank lattices to \(\mathrm{Out}{(F_N)}\) ⋮ Sublinearly Morse boundary. I: CAT(0) spaces ⋮ Roller boundaries for median spaces and algebras ⋮ Hyperbolicities in CAT(0) cube complexes ⋮ Proper proximality in non-positive curvature ⋮ Homotopy equivalent boundaries of cube complexes ⋮ Sublinearly Morse boundaries from the viewpoint of combinatorics ⋮ Isometric group actions with vanishing rate of escape on \(\mathrm{CAT}(0)\) spaces ⋮ Comparing topologies on the Morse boundary and quasi-isometry invariance ⋮ CAT(0) cube complexes are determined by their boundary cross ratio ⋮ Comparing the roller and \(B(X)\) boundaries of \(\operatorname{CAT}(0)\) cube complexes ⋮ Rank-one isometries of CAT(0) cube complexes and their centralisers ⋮ Superrigidity of actions on finite rank median spaces ⋮ Cross ratios and cubulations of hyperbolic groups ⋮ Cross‐ratios on CAT(0) cube complexes and marked length‐spectrum rigidity

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