Ratio limits and Martin boundary

  • Wolfgang Woess

    Institut für Diskrete Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
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Abstract

Consider an irreducible Markov chain which satisfies a ratio limit theorem, and let be the spectral radius of the chain. We investigate the relation of the the -Martin boundary with the boundary induced by the -harmonic kernel which appears in the ratio limit. Special emphasis is on random walks on non-amenable groups, specifically, free groups and hyperbolic groups.

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Wolfgang Woess, Ratio limits and Martin boundary. Doc. Math. 26 (2021), pp. 1501–1528

DOI 10.4171/DM/847