Random Walks on the Affine Group of a Homogeneous Tree in the Drift-Free Case

Dariusz Buraczewski () and Konrad Kolesko ()
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Dariusz Buraczewski: Uniwersytet Wrocławski
Konrad Kolesko: Uniwersytet Wrocławski

Journal of Theoretical Probability, 2012, vol. 25, issue 1, 189-204

Abstract: Abstract The affine group of a homogeneous tree is the group of all its isometries fixing an end of its boundary. We consider a random walk with law μ on this group and the associated random processes on the tree and its boundary. In the drift-free case there exists on the boundary of the tree a unique μ-invariant Radon measure. In this paper we describe its behaviour at infinity.

Keywords: Random walk; Affine group; Homogeneous tree; Invariant measure; 60B15 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-010-0323-6

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