The Martin boundary for general isotropic random walks in a tree

DOI10.1007/BF01046997zbMath0728.60013OpenAlexW2015954769MaRDI QIDQ805045

Donald I. Cartwright, Stanley A. Sawyer

Publication date: 1991

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01046997

zbMATH Keywords

Martin boundaryisotropic random walknearest neighbor harmonic functionsnon-abelian renewal theorynon-self intersecting path

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (8)

Path decompositions for Markov chains. ⋮ Convergence to Ends for Random Walks on the Automorphism Group of a Tree ⋮ The Martin boundary of a free product of abelian groups ⋮ The Dirichlet problem at infinity for random walks on graphs with a strong isoperimetric inequality ⋮ Ratio limits and Martin boundary ⋮ Positive harmonic functions of transformed random walks ⋮ Random walks on groups and KMS states ⋮ Ultrametric and tree potential

Cites Work

• Asymptotic behavior of successive coefficients of some power series
• The rate of escape for anisotropic random walks in a tree
• Random walks on discrete groups: Boundary and entropy
• An inversion formula for the Radon transform on trees
• Full Banach Mean Values on Countable groups.
• Isotropic random walks in a tree
• [https://portal.mardi4nfdi.de/wiki/Publication:4139440 Marche al�atoire sur le groupe libre et fronti�re de Martin]
• Martin Boundaries of Random Walks: Ends of Trees and Groups
• Convergence to Ends for Random Walks on the Automorphism Group of a Tree
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