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.
Cite this article
Wolfgang Woess, Ratio limits and Martin boundary. Doc. Math. 26 (2021), pp. 1501–1528
DOI 10.4171/DM/847