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Reinforced random walks and adic transformations. (English) Zbl 1217.37004

The aim of the present paper is to define and analyze several kinds of adic, Bratelli-Vershic systems such as stationary, symbol-count and reinforced related to walks on a finite, directed, strongly connected graph. The authors managed to give conditions for the natural walk measure to be adic-invariant and moreover to identify the ergodic adic-invariant measures for some classes of examples.

MSC:

37A30 Ergodic theorems, spectral theory, Markov operators
37A05 Dynamical aspects of measure-preserving transformations
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