Related papers: Random-like properties of chaotic forcing
Scattering off the edge of a composite particle or finite-range interaction can precede that off its center. An effective theory treatment with pointlike particles and contact interactions must find that the scattered experimental wave is…
We prove the Almost Sure Invariance Principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing…
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…
We obtain central limit theorem, local limit theorems and renewal theorems for stationary processes generated by skew product maps $T(\om,x)=(\te\om,T_\om x)$ together with a $T$-invariant measure, whose base map $\te$ satisfies certain…
We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity…
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…
A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes…
Shuffling-type gradient methods are favored in practice for their simplicity and rapid empirical performance. Despite extensive development of convergence guarantees under various assumptions in recent years, most require the Lipschitz…
We prove an exponential separation in sample complexity between Euclidean and hyperbolic representations for learning on hierarchical data under standard Lipschitz regularization. For depth-$R$ hierarchies with branching factor $m$, we…
We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicity along the leaves implies existence of a finite number of ergodic absolutely continuous invariant probability measures which describe the asymptotics of…
We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…
It is known that locally constant toral extensions of hyperbolic systems can never mix at an exponential rate. In this note we exhibit some examples of non-abelian locally constant compact extensions of the shift map which are exponentially…
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
The transfer operator corresponding to a uniformly expanding map enjoys good spectral properties. Here it is verified that coupling yields explicit estimates that depend continuously on the expansion and distortion constants of the map. For…
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical…
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…
Viable candidate theories for electroweak dynamical symmetry breaking are expected to show (near) conformal behaviour in order to accommodate current phenomenological constraints. In principle, renormalisation group studies using finite…
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…