Related papers: Weak Gibbs and Equilibrium Measures for Shift Spac…

We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of…

Given a factor code $\pi$ from a shift of finite type $X$ onto a sofic shift $Y$, an ergodic measure $\nu$ on $Y$, and a function $V$ on $X$ with summable variation, we prove an invariant upper bound on the number of ergodic measures on $X$…

Given an irreducible subshift of finite type X, a subshift Y, a factor map \pi : X \to Y, and an ergodic invariant measure \nu on Y, there can exist more than one ergodic measure on X which projects to \nu and has maximal entropy among all…

It is well known that the Gibbs inequality, which says that the Gibbs ratio is bounded above and below by positive constants, holds for the unique equilibrium states of H\"older continuous potentials on shift spaces, but it can fail for…

We provide a quantification of the uniqueness of Gibbs measure for topologically mixing countable Markov shifts with locally H\"older continuous potentials. Corollaries for speed of convergence for approximation by finite subsystems are…

Let $\pi:X\to Y$ be a factor map, where $(X,\sigma_X)$ and $(Y,\sigma_Y)$ are subshifts over finite alphabets. Assume that $X$ satisfies weak specification. Let $\ba=(a_1,a_2)\in \R^2$ with $a_1>0$ and $a_2\geq 0$. Let $f$ be a continuous…

We prove that ergodic measures on one-sided shift spaces are uniformly scaling in the sense of Gavish. That is, given a shift ergodic measure we prove that at almost every point the scenery distributions weakly converge to a common…

We prove that a shift ergodic measure on a topologically mixing sub-shift is isomorphic to a Bernoulli shift whenever it is quasi invariant under permutations of finite number of coordinates. We prove also that Gibbs measures on…

We prove a result on equilibrium measures for potentials with summable variation on arbitrary subshifts over a countable amenable group. For finite configurations $v$ and $w$, if $v$ is always replaceable by $w$, we obtain a bound on the…

It is known that the space of boundedly finite integer-valued measures on a complete separable metric space becomes itself a complete separable metric space when endowed with the weak-hash metric. It is also known that convergence under…

Let $(X,T)$ and $(Y,S)$ be two subshifts so that $Y$ is a factor of $X$. For any asymptotically sub-additive potential $\Phi$ on $X$ and $\ba=(a,b)\in\R^2$ with $a>0$, $b\geq 0$, we introduce the notions of $\ba$-weighted topological…

We consider equilibrium states (that is, shift-invariant Gibbs measures) on the configuration space $S^{\mathbb{Z}^d}$ where $d\geq 1$ and $S$ is a finite set. We prove that if an equilibrium state for a shift-invariant uniformly summable…

We consider the problem of equivalence of Gibbs states and equilibrium states for continuous potentials on full shift spaces $E^{\mathbb{Z}}$. Sinai, Bowen, Ruelle and others established equivalence under various assumptions on the…

We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy…

Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of…

We consider some of the main notions of Gibbs measures on subshifts introduced by different communities, such as dynamical systems, probability, operator algebras, and mathematical physics. For potentials with $d$-summable variation, we…

Let $\Phi$ be a unital positive linear map and let $A$ be a positive invertible operator. We prove that there exist partial isometries $U$ and $V$ such that \[ |\Phi(f(A))\Phi(A)\Phi(g(A))|\leq U^*\Phi(f(A)Ag(A))U \] and…

We characterize the finiteness of Gibbs measures for geodesic flows on negatively curved manifolds by several criteria, analogous to those proposed by Sarig for symbolic dynamical systems over an infinite alphabet. As an application, we…

We study the selfsimilarity and the Gibbs properties of several measures defined on the product space $\Omega\_r:=\{0,1,...,\break r-1\}^{\mathbb N}$. This space can be identified with the interval $[0,1]$ by means of the numeration in base…

In this article, we present some fixed point theorems in partially ordered G-metric space using the concept of $(\psi,\phi)$- weak contraction which extend many existing fixed point theorems in such space. We also give some examples to show…