Related papers: Ergodic properties of matrix equilibrium states

In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric $\alpha$-stable processes. For this purpose, explicit and sharp criteria for…

We contribute to the thermodynamic formalism of H\"older continuous fiber-bunched matrix cocycles, Anosov diffeomorphisms, and hyperbolic repellers. Specifically, we prove that $1$-typical fiber-bunched cocycles $\mathcal{A}$ over…

Let $M=X/\Gamma$ be a geometrically finite negatively curved manifold with fundamental group $\Gamma$ acting on $X$ by isometries. The purpose of this paper is to study the mixing property of the geodesic flow on $T^1M$, the asymptotic…

This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between…

We consider a chain of three rotors (rotators) whose ends are coupled to stochastic heat baths. The temperatures of the two baths can be different, and we allow some constant torque to be applied at each end of the chain. Under some…

In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to…

We prove almost sure ergodic theorems for a class of systems called quasistatic dynamical systems. These results are needed, because the usual theorem due to Birkhoff does not apply in the absence of invariant measures. We also introduce…

In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and…

We give explicit $C^1$-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with…

This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose the time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded…

Let $(\Omega, \P)$ be a standard probability space and let $\vartheta:\Omega \to \Omega$ be a measure preserving ergodic homeomorphism. Let $\mathcal{A}$ be a $C^*$-algebra with a unit and let $\mathcal{A}_{\mathbb{Z}}$ be the quasi-local…

Ergodicity of random dynamical systems with a periodic measure is obtained on a Polish space. In the Markovian case, the idea of Poincar\'e sections is introduced. It is proved that if the periodic measure is PS-ergodic, then it is ergodic.…

We consider a one-step matrix cocycle generated by a pair of non-negative parabolic matrices and study the equilibrium measures for $t\log \|\mathcal A\|$ as $t$ runs over the reals. We show that there is a freezing first order phase…

A subshift with linear block complexity has at most countably many ergodic measures, and we continue of the study of the relation between such complexity and the invariant measures. By constructing minimal subshifts whose block complexity…

Let $\Psi_n$ be a product of $n$ independent, identically distributed random matrices $M$, with the properties that $\Psi_n$ is bounded in $n$, and that $M$ has a deterministic (constant) invariant vector. Assuming that the probability of…

We prove the existence of a successful coupling for $n$ particles in the symmetric inclusion process. As a consequence we characterize the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in…

We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…

The current-carrying steady-state that arises in the middle of a metallic wire connected to macroscopic leads is characterized regarding its response functions, correlations and entanglement entropy. The spectral function and the dynamical…

Motivated by reformulating Furstenberg's $\times p,\times q$ conjecture via representations of a crossed product $C^*$-algebra, we show that in a discrete $C^*$-dynamical system $(A,\Gamma)$, the space of (ergodic) $\Gamma$-invariant states…

In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some cases, we also know that the maximizing measure has full…