Loss of Memory and Moment Bounds for Nonstationary Intermittent Dynamical Systems

Korepanov, Alexey; Leppänen, Juho

doi:10.1007/s00220-021-04071-5

Cited by 11 publications

(24 citation statements)

References 37 publications

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“…We note that H is well-defined since G is well-defined and due to (35). Some finer properties of G and H are given in the following result.…”

Section: An Auxiliary Regularity Resultsmentioning

confidence: 96%

“…Our construction of adapted norms is somewhat similar to the classical construction due to Pesin (see for example [5,Section 3]). However, our construction is different since besides transforming (30) and ( 31) into uniform type conditions (see (36) and ( 37)), an important feature of our adapted norms is given by properties (35) and (38). As we will see later on, these properties will be of central importance for our arguments.…”

Section: Adapted Normsmentioning

confidence: 99%

“…Among many remarkable contributions, we particularly emphasize those dealing with the decay of correlations [2,6,7,9,12,15], various (quenched or annealed) limit laws [1,4,16,17,18,19,20,30,31,32,39,43,44,48], as well as recent results devoted to the linear response of random dynamical systems [8,23,47]. For similar results in the closely related context of sequential dynamical systems, we refer to [10,11,33,35,36,37,29,42] and references therein.…”

Section: Introductionmentioning

confidence: 98%

“…that(35) and (56) imply thatX L itn,n ω (v 0 ω − v itn ω )dm = X L n ω (e itnSnψ(ω,•) (v 0 ω − v itn ω ))dm = X e itnSnψ(ω,•) (v 0 ω − v itn ω )dm ≤ − v itn S ,for P-a.e. ω ∈ Ω and n ∈ N. Thus, from Theorem 40 we conclude that lim n→∞ X L itn,n ω (v 0 ω − v itn ω )dm = 0, for P-a.e.…”

mentioning

confidence: 96%

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Quenched limit theorems for expanding on average cocycles

Dragičević¹,

Sedro²

2021

Preprint

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We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method for nonautonomous dynamics developed by Dragičević et al. (Comm Math Phys 360: 1121-1187, to deal with the case of random dynamics that exhibits nonuniform decay of correlations, which are ubiquitous in the context of the multiplicative ergodic theory. Our results provide an affirmative answer to a question posed by Buzzi (Comm Math Phys 208: 25-54, 1999).

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“…We note that H is well-defined since G is well-defined and due to (35). Some finer properties of G and H are given in the following result.…”

Section: An Auxiliary Regularity Resultsmentioning

confidence: 96%

Section: Adapted Normsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

mentioning

confidence: 96%

See 2 more Smart Citations

Quenched limit theorems for expanding on average cocycles

Dragičević¹,

Sedro²

2021

Preprint

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“…Remark 1.1. After we finished this work, we learned about a preprint by Korepanov and Leppänen [KL20] in which interesting related results are obtained.…”

Section: Large Deviations and Clts For Intermittent Maps 2807mentioning

confidence: 99%

Large deviations and central limit theorems for sequential and random systems of intermittent maps

Nicol¹,

Pereira²,

Török

2020

Ergod. Th. Dynam. Sys.

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We obtain large and moderate deviation estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems obtained by Nicol, Török and Vaienti [Central limit theorems for sequential and random intermittent dynamical systems. Ergod. Th. & Dynam. Sys.38(3) (2018), 1127–1153] for random dynamical systems comprising intermittent maps. Using recent work of Abdelkader and Aimino [On the quenched central limit theorem for random dynamical systems. J. Phys. A 49(24) (2016), 244002] and Hella and Stenlund [Quenched normal approximation for random sequences of transformations. J. Stat. Phys.178(1) (2020), 1–37] we extend the results of Nicol, Török and Vaienti on quenched central limit theorems for centered observables over random compositions of intermittent maps: first by enlarging the parameter range over which the quenched central limit theorem holds; and second by showing that the variance in the quenched central limit theorem is almost surely constant (and the same as the variance of the annealed central limit theorem) and that centering is needed to obtain this quenched central limit theorem.

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Sunklodas’ Approach to Normal Approximation for Time-Dependent Dynamical Systems

Leppänen¹,

Stenlund

2020

J Stat Phys

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We adapt Stein's method to obtain Berry-Esseen type error bounds in the multivariate central limit theorem for non-stationary processes generated by timedependent compositions of uniformly expanding dynamical systems. In a particular case of random dynamical systems with a strongly mixing base transformation, we derive an error estimate of order O(N −1/2 ) in the quenched multivariate CLT, provided that the covariance matrix "grows linearly" with the number of summands N . The error in the normal approximation is estimated for the class of all convex sets.

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Loss of Memory and Moment Bounds for Nonstationary Intermittent Dynamical Systems

Cited by 11 publications

References 37 publications

Quenched limit theorems for expanding on average cocycles

Quenched limit theorems for expanding on average cocycles

Large deviations and central limit theorems for sequential and random systems of intermittent maps

Sunklodas’ Approach to Normal Approximation for Time-Dependent Dynamical Systems

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