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Substitution Markov chains and Martin boundaries. (English) Zbl 1406.60112

Summary: Substitution Markov chains have been introduced [the first author, Substitution Markov chains with applications to molecular evolution. State College, PA: Pennsylvania State University (PhD Thesis) (2012)] as a new model to describe molecular evolution. In this note, we study the associated Martin boundaries from a probabilistic and topological viewpoint. An example is given that, although having a boundary homeomorphic to the well-known coin tossing process, has a metric description that differs significantly.

MSC:

60J50 Boundary theory for Markov processes
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
31C35 Martin boundary theory
37A50 Dynamical systems and their relations with probability theory and stochastic processes
28D05 Measure-preserving transformations
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