Ratio limits and Martin boundary

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

No reviews yet.

No comments yet.