Related papers: Recurrence and pressure for group extensions

Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties…

There has been much interest in generalizing Kesten's criterion for amenability in terms of a random walk to other contexts, such as determining amenability of a deck covering group by the bottom of the spectrum of the Laplacian or entropy…

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 asymmetry in the…

Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric…

Symbolic dynamical theory plays an important role in the research of amenability with a countable group. Motivated by the deep results of Dougall and Sharp, we study the group extensions for topologically mixing random shifts of finite…

We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for…

We characterise amenability of a countable group in terms of the spectral radius of the Perron-Frobenius operator associated to a group extension of a countable Markov shift and a H\"older continuous potential. This extends a result of Day…

We define a class of discrete abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply…

We study hyperbolic attractors of some dynamical systems with apriori given countable Markov partitions. Assuming that contraction is stronger than expansion we construct new Markov rectangles such that their crossections by unstable…

We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to…

We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such…

We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This covers amenability of a wide class groups, the amenability of which…

For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for…

We give a set of equivalent conditions for a potential on a Countable Markov Shift to have strong positive recurrence, which is also equivalent to having exponential decay of correlations. A key ingredient of our proofs is quantifying how…

We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and…

We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many…

We introduce a definition of pressure for almost-additive sequences of continuous functions defined over (non-compact) countable Markov shifts. The variational principle is proved. Under certain assumptions we prove the existence of Gibbs…

We consider a robust class of random non-uniformly expanding local homeomorphisms and H\"older continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and…

In this paper, we introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure for continuous actions of countable amenable groups on such…

In this article, we study the pressure at infinity of potentials defined over countable Markov shifts. We establish an upper semi-continuity result concerning the limiting behaviour of the pressure of invariant probability measures, where…