Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems
Ian Melbourne,Matthew Nicol +1 more
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In this paper, the authors prove an almost sure invariance principle for general classes of nonuniformly expanding and non-uneiformly hyperbolic dynamical systems, and apply it to planar periodic Lorentz flows with finite horizon.Abstract:
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result applies to the planar periodic Lorentz flow with finite horizon. Statistical limit laws such as the central limit theorem, the law of the iterated logarithm, and their functional versions, are immediate consequences.read more
Citations
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Large deviations for nonuniformly hyperbolic systems
Ian Melbourne,Matthew Nicol +1 more
TL;DR: In this paper, large deviation estimates for a large class of nonuniformly hyperbolic systems with summable decay of correlations were obtained, namely those modelled by Young towers.
Journal ArticleDOI
The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
TL;DR: In this paper, the Boltzmann-Grad limit for the free path length of a point particle in a periodic array of spherical scatterers is investigated, where the radius of each scatterer tends to zero.
Journal ArticleDOI
Large deviations in non-uniformly hyperbolic dynamical systems
Luc Rey-Bellet,Lai Sang Young +1 more
TL;DR: In this article, large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times were proved for piecewise hyperbolic diffeomorphisms, dispersing billiards including Lorentz gases, and strange attractors of rank one including Hattractors.
Journal ArticleDOI
A vector-valued almost sure invariance principle for hyperbolic dynamical systems
Ian Melbourne,Matthew Nicol +1 more
TL;DR: In this article, the authors prove an almost sure invariance principle for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems, including Axiom A dieomorphisms and flows as well as systems modelled by Young towers.
Posted Content
The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
TL;DR: In this paper, the Boltzmann-Grad limit for the free path length of the periodic Lorentz gas was investigated and the existence of a limiting distribution for free path lengths of the gas was proved.
References
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