Geodesic
Ratio limits and Martin boundary
Documenta mathematica, Tome 26 (2021), pp. 1501-1528.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 60J50, 60G50, 60J10
Keywords: random walk, ratio limit, \(\rho\)-harmonic functions, Martin boundary 
@article{DOCMA_2021__26__a17,
     author = {Woess, Wolfgang},
     title = {Ratio limits and {Martin} boundary},
     journal = {Documenta mathematica},
     pages = {1501--1528},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a17/}
}
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Woess, Wolfgang. Ratio limits and Martin boundary. Documenta mathematica, Tome 26 (2021), pp. 1501-1528. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a17/