Related papers: Mixing for some non-uniformly hyperbolic systems

This paper addresses the three concepts of \textit{ consistency, stability and convergence } in the context of compact finite volume schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of…

In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for…

We develop Markov chain mixing time estimates for a class of Markov chains with restricted transitions. We assume transitions may occur along a cycle of $n$ nodes and on $n^\gamma$ additional edges, where $\gamma < 1$. We find that the…

We investigate dynamical systems obtained by coupling two maps, one of which is chaotic and is exemplified by an Anosov diffeomorphism, and the other is of gradient type and is exemplified by a N-pole-to-S-pole map of the circle. Leveraging…

Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embeddings…

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…

We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…

This paper will provide several classes of strictly stationary, countable-state, irreducible, aperiodic Markov chains that are reversible and have finite second moments, such that the central limit theorem fails to hold. The main purpose is…

We obtain estimates on the decay of correlations, Central Limit Theorem and Large Deviations for dynamical systems admitting an induced weak Gibbs--Markov map, for larger classes of observables with weaker regularity than H\"{o}lder,…

We establish some statistical properties of the hyperbolic times for a class of nonuniformly expanding dynamical systems. The maps arise as factors of area preserving maps of the unit square via a geometric Baker's map type construction,…

We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…

In 2019 Anthony Quas, Philippe Thieullen and Mohamed Zarrabi introduced the concept of strong fast invertibility for linear cocycles. It relates the growth of volumes between different initial times and, together with a condition on…

In many strongly-coupled systems, the infrared dynamics is described by different degrees of freedom from the ultraviolet. It is then natural to ask how operators written in terms of the microscopic variables are mapped to operators…

We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have different rates of decay of correlations and how this may…

We investigate the shrinking target and recurrence set associated to non-autonomous measure-preserving systems on compact metric spaces, establishing zero-one criteria in the spirit of classical Borel-Cantelli results. Our first main…

This paper provides a general and abstract approach to approximate ergodic regimes of Markov and Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton & Pages (2002) and based on simulation algorithms…

We prove the almost sure invariance principle with rate $o(n^{\varepsilon})$ for every $\varepsilon > 0$ for H\"older continuous observables on nonuniformly expanding and nonuniformly hyperbolic transformations with exponential tails.…

Model-based clustering imposes a finite mixture modelling structure on data for clustering. Finite mixture models assume that the population is a convex combination of a finite number of densities, the distribution within each population is…

Here we propose the Donsker-Varadhan-type compactness conditions and prove the joint large deviation principle for the empirical measure and empirical flow of Markov renewal processes (semi-Markov processes) with a countable state space,…

We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical…