Sharp polynomial estimates for the decay of correlations

By S. Gouëzel. 2002

131 citations recorded by the source corpus.

We generalize a method developed by Sarig to obtain polynomial lower bounds for correlation functions for maps with a countable Markov partition. A consequence is that LS Young’s estimates on towers are always optimal. Moreover, we show that, for functions with zero average, the decay rate is better, gaining a factor 1 /n . This implies a Central Limit Theorem in contexts where it was not expected, e.g. x + Cx 1+ α with 1 / 2 6 α < 1. The method is based on a general result on renewal sequences of operator, and gives an asymptotic estimate up to any precision of such operators.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/36582cf303ca78598efa93d05192978c4330c679

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Operator renewal theory and mixing rates for dynamical systems with infinite measure (2010, methodology): “Proof Since the details can be found in [18, 37], we only sketch the argument.”
STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS WITH CRITICAL POINTS AND SINGULARITIES (2006, methodology): “An approach for analysing mixing rates using the Gibbs-Markov formalism has been developed in [16, 44].”
Chapter 2 – Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics (2006, methodology): “This is often enough to determine Cov(f, g ◦Tn) up to asymptotic equivalence (see [223],[99] for examples).”
Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows (2006, methodology): “Following Sarig [31] (see also [20, 10]) we define Ts,n : L(1)(Y ) → L(1)(Y ) and Rs,n : L(1)(Y ) → L(1)(Y ) by Ts,nv = 1Y Ls (1Y v), Rs,nv = 1Y L n s (1Znv).”
Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains (2009, methodology): “This spectral control makes it possible to apply Theorem 1.1 in Gouëzel (2004b), dealing with renewal sequences of operators as above.”