Almost sure invariance principle for random piecewise expanding maps

Dragičević, Davor; Froyland, Gary; González-Tokman, Cecilia; Vaienti, Sandro

doi:10.1088/1361-6544/aaaf4b

Cited by 59 publications

(114 citation statements)

References 38 publications

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“…Recently there has been a remarkable interest in studying statistical limit theorems for random dynamical systems [1,4,5,9,10,12,13,15,21]. Most of these results assume some knowledge about the rate of correlation decay of the random system under consideration.…”

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confidence: 99%

Quenched decay of correlations for slowly mixing systems

Bahsoun¹,

Bose²,

Ruziboev³

2019

Trans. Amer. Math. Soc.

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We study random towers that are suitable to analyse the statistics of slowly mixing random systems. We obtain upper bounds on the rate of quenched correlation decay in a general setting. We apply our results to the random family of Liverani-Saussol-Vaienti maps with parameters in [α 0 , α 1 ] ⊂ (0, 1) chosen independently with respect to a distribution ν on [α 0 , α 1 ] and show that the quenched decay of correlation is governed by the fastest mixing map in the family. In particular, we prove that for every δ > 0, for almost every ω ∈ [α 0 , α 1 ] Z , the upper bound n 1− 1 α 0 +δ holds on Date: January 30, 2018. 1991 Mathematics Subject Classification. Primary 37A05, 37E05. Key words and phrases. Random dynamical systems, slowly mixing systems, quenched decay of correlations.

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confidence: 99%

Quenched decay of correlations for slowly mixing systems

Bahsoun¹,

Bose²,

Ruziboev³

2019

Trans. Amer. Math. Soc.

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“…Quenched limit theorems for random dynamical systems are abundant in the literature, going back at least to Kifer [14]. Nevertheless they remain a lively topic of research to date: Recent central limit theorems and invariance principles in such a setting include Ayyer-Liverani-Stenlund [4], Nandori-Szasz-Varju [17], Aimino-Nicol-Vaienti [2], Abdelkader-Aimino [1], Nicol-Török-Vaienti [18], Dragičević et al [9,10], and Chen-Yang-Zhang [8]. Moreover, Bahsoun et al [5][6][7] establish important optimal quenched correlation bounds with applications to limit results, and Freitas-Freitas-Vaienti [11] establish interesting extreme value laws which have attracted plenty of attention during the past years.…”

Section: The Problemmentioning

confidence: 99%

Quenched Normal Approximation for Random Sequences of Transformations

Hella

Stenlund

2019

J Stat Phys

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We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the multivariate case, assuming fiberwise centering. For the most part we work with non-stationary randomness and non-invariant, non-product measures. Independently, we believe our work sheds light on the mechanisms that make quenched central limit theorems work, by dissecting the problem into three separate parts.

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“…Quenched limit theorems for random dynamical systems have been established in many articles. We mention [1,3,6,11,14,15] as examples of recent works in this area. In [35], a quenched CLT for i.i.d selections of intermittent maps belonging to a finite set of maps was established.…”

Section: Introductionmentioning

confidence: 99%

Central limit theorems with a rate of convergence for time-dependent intermittent maps

Hella

Leppänen

2019

Stoch. Dyn.

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We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate of convergence. For maps chosen from a certain parameter range, but without additional assumptions on how the maps vary with time, we obtain a self-norming CLT provided that the variances of the partial sums grow sufficiently fast. When the maps are chosen randomly according to a shift-invariant probability measure, we identify conditions under which the quenched CLT holds, assuming fiberwise centering. Finally, we show a multivariate CLT for intermittent quasistatic systems. Our approach is based on Stein's method of normal approximation.Acknowledgements. The authors would like to thank Mikko Stenlund for helpful comments on preliminary versions of the manuscript.

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Almost sure invariance principle for random piecewise expanding maps

Cited by 59 publications

References 38 publications

Quenched decay of correlations for slowly mixing systems

Quenched decay of correlations for slowly mixing systems

Quenched Normal Approximation for Random Sequences of Transformations

Central limit theorems with a rate of convergence for time-dependent intermittent maps

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