My question is about the following article:
https://arxiv.org/pdf/2002.10278.pdf
On page 34 the autors talk about the Markov property of hyperbolic groups. In particular , they say that the Cayleygraph of $\Gamma$ (which is a non-elementary hyperbolic group) has this Markov property but the Cayleygraphs of the supgroups of $\Gamma$ do not have it.
In the following article (2.2) I found a definition for Markov chains on groups:
https://arxiv.org/pdf/2111.09837.pdf
Unfortunatly I do not know how to transfer this definition to the context of the first article. Ans I also dont know why the Cayleygraph of $\Gamma$ (which is a non-elementary hyperbolic group) has this Markov property but the Cayleygraphs of the supgroups of $\Gamma$ do not have it.
Does anybody have an idea?