Subexponential decay of correlations

By O. Sarig. 2002

216 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/522d1ab03011eb4c96db70f23f151a916db423ca

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Polynomial loss of memory for maps of the interval with a neutral fixed point (2014, background): “Note that, by the results of [13], one cannot have in general a faster than polynomial decay, because that is the (sharp) rate when iterating a single map T , 0 < < 1.”
Billiards with polynomial mixing rates (2004, result): “We only point out recent results by Sarig in this direction [20].”
Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains (2009, methodology): “Since this follows closely from the arguments in Sarig (2002), Gouëzel (2004b) and Gouëzel (2007), we will only sketch the proof.”
Sharp polynomial estimates for the decay of correlations (2002, methodology): “in O(1/nβ) if R f = 0 (see Theorem 6.9 and Proposition 6.11). This kind of results is useful in the proof of the Central Limit Theorem. The following corollaries are already present in weaker form in [Sar], where the notations are explained. Some details on their proofs will be given in the last sec”
Operator renewal theory and mixing rates for dynamical systems with infinite measure (2010, methodology): “Sarig [37] introduced a powerful new technique, operator renewal theory, to obtain precise asymptotics and hence sharp mixing rates.”
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).”
Chapter 2 – Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics (2006, methodology): “We would like to thank O. Sarig who provided us the text for Section 18.”
From rates of mixing to recurrence times via large deviations (2010, background): “s-Markov induced map with exponential tail of the return times. By [Yo2] this implies exponential decay of correlations for all H¨older continuous observables. However, it is proved in [Hu], see also [Sar], that the decay of correlations cannot be faster than polynomial: there exist Lipschitz functi”
Berry-Esseen theorem and local limit theorem for non uniformly expanding maps (2003, methodology): “We will use the same kind of perturbative ideas as in [30] and [17], but applied to transfer operators associated to induced maps on the basis B of the tower (see [32]).”
Central limit theorem and stable laws for intermittent maps (2002, methodology): “For these definitions, see for example [ADU93], [Aar97] or [ Sar02 ].”
Markov structures and decay of correlations for non-uniformly expanding dynamical systems☆ (2002, result): “However the constructions always give rise to countable partitions and any conclusions about the invariant measures and other statistical properties then depends on a corresponding ergodic theory for countable subshifts which is much less developed than the finite case, although some results exist, ”