2009/05/31 by Camille Petit
Mathematics · #Almost everywhere #Curvature #Discrete mathematics #Function (biology) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Graph #Harmonic function #Mathematical analysis #Mathematics #Negative curvature #Pure mathematics #Random walk #Scalar curvature #Sectional curvature #advanced mathematical theories #math.MG #math.PR
paper · pdf · doi:10.1090/s0002-9939-2011-10931-6
published as Proc. Amer. Math. Soc. 140 (2012) 235-248 · 14 pages
openalex publication_date 2011/05/17 · arxiv created 2013/03/11 · arxiv updated 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The proof is inspired by the works of F. Mouton in the cases of Riemannian manifolds of pinched negative curvature and infinite trees. It involves geometric and probabilitistic methods.