Related papers: Quenched Mixing Rates for Doubly Intermittent Maps

We consider independently identically distributed random compositions of the Gauss and R\'enyi maps that generate random continued fractions. Using methods of ergodic theory, thermodynamic formalism and large deviations, we show that…

We study a random map $T$ which consists of intermittent maps $\{T_{k}\}_{k=1}^{K}$ and a position dependent probability distribution $\{p_{k,\varepsilon}(x)\}_{k=1}^{K}$. We prove existence of a unique absolutely continuous invariant…

We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on…

We study a class of random transformations built over finitely many intermittent maps sharing a common indifferent fixed point. Using a Young-tower technique, we show that the map with the fastest relaxation rate dominates the asymptotics.…

We prove the one-dimensional almost sure invariance principle with essentially optimal rates for slowly (polynomially) mixing deterministic dynamical systems, such as Pomeau-Manneville intermittent maps, with H\"older continuous…

We prove general mixing theorems for sequences of meromorphic maps on compact K\"ahler manifolds. We deduce that the bifurcation measure is exponentially mixing for a family of rational maps of $\mathbb{P}^q(\mathbb{C})$ endowed with…

This article describes the quenched localisation behaviour of the Bouchaud trap model on the integers with regularly varying traps. In particular, it establishes that for almost every trapping landscape there exist arbitrarily large times…

As we all known, there is still a long way for us to solve arbitrary multivariate Lagrange interpolation in theory. Nevertheless, it is well accepted that theories about Lagrange interpolation on special point sets should cast important…

We derive rates of convergence for the mixing of operators under infinitely divisible measures in the framework of linear dynamics on Banach spaces. Our approach is based on the characterization of mixing in terms of codifference…

We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation…

We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…

In this work, we consider i.i.d. random perturbations of contracting Lorenz maps sufficiently close to a Rovella parameter. We prove that the quenched correlations of the random dynamical system decay exponentially.

Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function…

We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a…

We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying…

Globally coupled doubling maps are studied in this paper. In this setting and for finitely many sites, two distinct bifurcation values of the coupling strength have been identified in the literature, corresponding to the emergence of…

In the context of 'infinite-volume mixing' we prove global-local mixing for the Boole map, a.k.a. Boole transformation, which is the prototype of a non-uniformly expanding map with two neutral fixed points. Global-local mixing amounts to…

We consider a Lebesgue measure preserving map of the 2-torus, given by the composition of orthogonal tent shaped shears. We establish strong mixing properties with respect to the invariant measure and polynomial decay of correlations for…

Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay…

We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that…