Ratio limits and Martin boundary

Wolfgang Woess

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arXiv · 2104.11477

Ratio limits and Martin boundary

Wolfgang Woess

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Abstract

Consider an irreducible Markov chain which satisfies a ratio limit theorem, and let $\rho$ be the spectral radius of the chain. We investigate the relation of the the $\rho\,$-Martin boundary with the boundary induced by the $\rho\,$-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. 2021-04-23. Ratio limits and Martin boundary. https://arxiv.org/abs/2104.11477

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