The main results of this note extend a theorem of Kesten for symmetric random walks on discrete groups to group extensions of topological Markov chains. In contrast to the result in probability theory, there is a notable ...

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding ...

Consider the basic algorithm to perform the transformation n bar right arrow n + 1 changing digits of the d-adic expansion of n one by one. We obtain a family of Markov chains on the non-negative integers through successive ...

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined ...

In this work we define a stochastic adding machine associated to a quadratic base (F-n) (n >= 0) formed by recurrent sequences of order 2. We obtain a Markov chain with states in Z(+) and we prove that the spectrum of the ...

In this paper, we define some Markov chains associated with Vershik maps on Bratteli diagrams. We study probabilistic and spectral properties of their transition operators and we prove that the spectra of these operators ...

In this paper, we define some Markov chains associated with Vershik maps on Bratteli diagrams. We study probabilistic and spectral properties of their transition operators and we prove that the spectra of these operators ...