Related papers: Exponential decay of correlations for random inter…

Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and…

We show that any surface admits an area preserving $C^{1+\beta}$ diffeomorphism with non-zero Lyapunov exponents which is Bernoulli and has polynomial decay of correlations. We establish both upper and lower polynomial bounds on…

How can we interpret the infimum of Lipschitz constants in a conjugacy class of interval maps? For positive entropy maps, the exponential of the topological entropy gives a well-known lower bound. We show that for piecewise monotone…

We consider a large class of 2D area-preserving diffeomorphisms that are not uniformly hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A prime example is the Standard map. Lower bounds for…

We prove the exponential decay of correlations for C^\alpha-observables (0<\alpha =<2) for generic birational maps of P^k \`a la Bedford-Diller. In the particular case of regular birational maps, we give a better estimate of the speed of…

We study the set of points returning infinitely often to a sequence of targets dependent on the starting points. With an assumption of decay of correlations for L1 against bounded variations, we prove a generalized quantitative recurrence…

We consider Gaussian graphical models associated with an equicorrelational and one-dimensional conditional independence graph. We show that pairwise correlation decays exponentially as a function of distance. We also provide a limit when…

We prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency…

We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as…

The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the…

We consider multimodal C^3 interval maps f satisfying a summability condition on the derivatives D_n along the critical orbits which implies the existence of an absolutely continuous f -invariant probability measure mu. If f is…

We investigate certain large deviation asymptotics concerning random interlacements in Z^d, d bigger or equal to 3. We find the principal exponential rate of decay for the probability that the average value of some suitable non-decreasing…

We show that any $L^2$ solution of the Gabitov-Turitsyn equation describing dispersion managed solitons decay exponentially in space and frequency domains. This confirms in the affirmative Lushnikov's conjecture of exponential decay of…

For a class of tight-binding many-electron models on hyper-cubic lattices the equal-time correlation functions at non-zero temperature are proved to decay exponentially in the distance between the center of positions of the electrons and…

We consider pairs of toral automorphisms (A,B) satisfying an invariant cone property. At each iteration, A acts with probability p and B with probability 1-p. We prove exponential decay of correlations for a class of Holder continuous…

We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) a certain random variable on the…

We consider random perturbations of non-uniformly expanding maps, possibly having a non-degenerate critical set. We prove that, if the Lebesgue measure of the set of points failing the non-uniform expansion or the slow recurrence to the…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

We study synchronization of random one-dimensional linear maps for which the Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of these maps are explained using their relation with a random walk. We confirm that…

The two-dimensional random-bond Ising model is numerically studied on long strips by transfer-matrix methods. It is shown that the rate of decay of correlations at criticality, as derived from averages of the two largest Lyapunov exponents…