Renewal Theory on the Affine Group of an Oriented Tree

S. Brofferio
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S. Brofferio: Technische Universtät Graz

Journal of Theoretical Probability, 2004, vol. 17, issue 4, 819-859

Abstract: Abstract The affine group of a tree is the group of the isometries of a homogeneous tree that fix an end of its boundary. Consider a probability measure μ on this group and the associated random walk. The main goal of this paper is to determine the accumulation points of the potential kernel $$g * U = g * \sum\limits_{n = 0}^\infty {\mu ^{(n)} ,}$$ when g tends to infinity. In particular we show that under suitable regularity hypotheses this kernel can be continuously extended to the tree's boundary and we determine the limit measures.

Keywords: Random walk; renewal theory; affine group; tree; p-adic rationals (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s10959-004-0577-y

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