Boundary values, random walks, and \(\ell^p\)-cohomology in degree one

DOI10.4171/GGD/337zbMath1382.20052arXiv1303.4091MaRDI QIDQ902294

Antoine Gournay

Publication date: 8 January 2016

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.4091

zbMATH Keywords

Poisson boundaryharmonic functions\(L^p\)-cohomologygroup cohomohology

Mathematics Subject Classification ID

Cohomology of groups (20J06) Probabilistic potential theory (60J45) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Boundary theory for Markov processes (60J50) Means on groups, semigroups, etc.; amenable groups (43A07) Random walks on graphs (05C81)

Related Items (3)

Absence of non-constant harmonic functions with \(\ell^p\)-gradient in some semi-direct products ⋮ Harmonic functions with finite \(p\)-energy on lamplighter graphs are constant ⋮ Linear and Nonlinear Harmonic Boundaries of Graphs; An Approach with ℓ p-Cohomology in Degree One

Cites Work

• Unnamed Item
• Amenability via random walks.
• The wreath product of $\mathbb {Z}$ with $\mathbb {Z}$ has Hilbert compression exponent $\frac {2}{3}$

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