Krickeberg mixing for $${{\mathbb {Z}}}$$-extensions of Gibbs Markov semiflows

Terhesiu, Dalia

doi:10.1007/s00605-022-01693-2

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…We remark that mixing of the type of Corollary 2.3 has been previously obtained in [35] for Z-extensions of Gibbs Markov semiflows with roof and displacement functions in the domain of a nonstandard CLT. The method of proof in [35] is very different; in particular, it does not go via a MLLT for the base map.…”

Section: Remark 24supporting

confidence: 56%

Strong mixing for the periodic Lorentz gas flow with infinite horizon

Pène¹,

Terhesiu²

2023

Preprint

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We establish strong mixing for the Z d -periodic, infinite horizon, Lorentz gas flow for continuous observables with compact support. The essential feature of this natural class of observables is that their support may contain points with infinite free flights. Dealing with such a class of functions is a serious challenge and there is no analogue of it in the finite horizon case. The mixing result for the aforementioned class of functions is obtained via new results: 1) mixing for continuous observables with compact support consisting of configurations at a bounded time from the closest collision; 2) a tightness-type result that allows us to control the configurations with long free flights. To prove 1), we establish a mixing local limit theorem for the Sinai billiard flow with infinite horizon, previously an open question.

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Section: Remark 24supporting

confidence: 56%

Strong mixing for the periodic Lorentz gas flow with infinite horizon

Pène¹,

Terhesiu²

2023

Preprint

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“…For flows, the leading term has been studied in e.g. [2,9,17,30]. We also mention that there are other quantities besides the correlation functions whose asymptotic expansions are of interest.…”

mentioning

confidence: 99%

Asymptotic expansion of correlation functions for Zd covers of hyperbolic flows

Dolgopyat

Nándori

Pène

2022

Ann. Inst. H. Poincaré Probab. Statist.

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“…Krickeberg mixing and the related local limit theorems have been investigated for several (non-uniformly) hyperbolic systems, see, e.g. [1,8,11,12,17,25,26] and references therein. For the geodesic flow {g t } t∈R on a Z d -cover M 0 of M, Oh and Pan [19] showed that…”

Section: Introductionmentioning

confidence: 99%

Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows

Flaminio,

Ravotti

2024

Nonlinearity

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We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on Z d -covers, thus proving a strong form of Krickeberg mixing. We also prove that the spectral measures around 0 of the Casimir operators on any increasing sequence of finite Abelian covers converge weakly to an absolutely continuous measure.

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Krickeberg mixing for $${{\mathbb {Z}}}$$-extensions of Gibbs Markov semiflows

Abstract: We obtain Krickeberg mixing for a class of $${{\mathbb {Z}}}$$ Z -extensions of Gibbs Markov semiflows with roof function and displacement function not in $$L^2$$ L 2 , where previous methods fail. This is done via a ‘smooth tail’ estimate for the isomorphic suspension flow.

Cited by 3 publications

References 24 publications

Strong mixing for the periodic Lorentz gas flow with infinite horizon

Strong mixing for the periodic Lorentz gas flow with infinite horizon

Asymptotic expansion of correlation functions for Zd covers of hyperbolic flows

Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows

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