Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas
Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas
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DOI：
10.1088/1361-6544/ab7d22
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发表时间：
2019-01
期刊：
影响因子：
1.7
通讯作者：
Mark F. Demers;I. Melbourne;M. Nicol
中科院分区：
文献类型：
--
作者：
Mark F. Demers;I. Melbourne;M. Nicol
在本文中，我们展示了如何Gordin鞅逼近方法适合于各向异性的Banach空间框架。特别地，对于有限水平平面周期洛伦兹气体的时间一映射，我们证明了Hölder观测量满足统计极限定律，如中心极限定理和相关的不变性原理。在此之前，这些属性仅限于一类有限的可观测量，不包括例如速度。
In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Hölder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles. Previously, these properties were known only for a restricted class of observables, excluding for instance velocity.