Remarks on random walks on graphs and the Floyd boundary

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Abstract

We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, p (n) (v, w)≤Cρ n, where ρ<1 is the spectral radius, then for any Floyd function f that satisfies ∞ n=1 nf(n)<∞, the Dirichlet problem with respect to the Floyd boundary is solvable.

Original languageEnglish
Pages (from-to)183-194
Number of pages12
JournalArkiv för Matematik
Volume60
Issue number1
DOIs
Publication statusPublished - 16 May 2022

ASJC Scopus subject areas

  • Mathematics(all)

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