Martin Boundaries of Random Walks: Ends of Trees and Groups

DOI10.2307/2000905zbMath0615.60068OpenAlexW4214556682MaRDI QIDQ4722957

Massimo A. Picardello, Wolfgang Woess

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000905

zbMATH Keywords

Martin boundaryCayley graphsMartin kernelMartin compactificationrandom walk on a graph

Mathematics Subject Classification ID

Trees (05C05) Sums of independent random variables; random walks (60G50) Geometric group theory (20F65) Measures on groups and semigroups, etc. (43A05) Boundary theory for Markov processes (60J50)

Related Items (19)

The rate of escape for anisotropic random walks in a tree ⋮ The Martin boundary for harmonic functions on groups of automorphisms of a homogeneous tree ⋮ Heat kernel and Green kernel comparison theorems for infinite graphs ⋮ The Hausdorff dimension of the harmonic measure for relatively hyperbolic groups ⋮ Graphs and groups with tree-like properties ⋮ Martin boundaries of the duals of free unitary quantum groups ⋮ Harmonic functions on infinite graphs ⋮ Martin boundary covers Floyd boundary ⋮ Harmonic functions on Cartesian products of trees with finite graphs ⋮ The Dirichlet problem at infinity for random walks on graphs with a strong isoperimetric inequality ⋮ Ratio limits and Martin boundary ⋮ A decreasing rearrangement for functions on homogeneous trees ⋮ Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs ⋮ The Poisson boundary of covering Markov operators ⋮ Boundaries of random walks on graphs and groups with infinitely many ends ⋮ Ultrametric and tree potential ⋮ A Converse to the Mean Value Property on Homogeneous Trees ⋮ Probability measures on groups and some related ideals in group algebras ⋮ The Martin boundary for general isotropic random walks in a tree

Cites Work

• Martin boundaries of random walks on Fuchsian groups
• Simple random walks on trees
• Random walks on discrete groups: Boundary and entropy
• Non-negative matrices and Markov chains. 2nd ed
• Über die Enden diskreter Räume und Gruppen
• Extensions of Jentzsch's Theorem
• Full Banach Mean Values on Countable groups.
• Symmetric Random Walks on Groups
• [https://portal.mardi4nfdi.de/wiki/Publication:4139440 Marche al�atoire sur le groupe libre et fronti�re de Martin]
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