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Refined central limit theorem and infinite density tail of the Lorentz gas from Lévy walk
Journal of Physics A: Mathematical and Theoretical ( IF 2.1 ) Pub Date : 2020-09-17 , DOI: 10.1088/1751-8121/abadb6
Itzhak Fouxon 1, 2 , Peter Ditlevsen 2
Affiliation  

We consider point particle that collides with a periodic array of hard-core elastic scatterers where the length of the free flights is unbounded due to infinitely long corridors between the scatterers (the infinite-horizon Lorentz gas, LG). The Bleher central limit theorem (CLT) states that the distribution of the particle displacement divided by ##IMG## [http://ej.iop.org/images/1751-8121/53/41/415004/aabadb6ieqn1.gif] {$\sqrt{t\enspace \mathrm{ln}t}$} is Gaussian in the limit of infinite time t . However this result, describing the bulk of the distribution, is not as powerful as in normal diffusion cases. The Gaussian peak fails to describe the displacement’s moments of order higher than two and gives only half of the true value of the dispersion. These demand the tail of the distribution which is formed by rare long flights along the corridors where the particle propagates much further than in typical diffusive displacements due to collisions with ...

中文翻译:

Lévywalk的Lorentz气体的精确中心极限定理和无限密度尾巴

我们考虑与质点弹性散射体的周期性阵列碰撞的点粒子,由于散射体之间的无限长的长廊,自由飞行的长度不受限制(无限水平洛伦兹气体,LG)。Bleher中心极限定理(CLT)指出,粒子位移的分布除以## IMG ## [http://ej.iop.org/images/1751-8121/53/41/415004/aabadb6ieqn1.gif] {$ \ sqrt {t \ enspace \ mathrm {ln} t} $}在无限大的时间t的极限内是高斯。但是,描述大部分分布的结果并不像正常扩散情况那样强大。高斯峰无法描述位移矩大于2的量级,并且仅给出色散真实值的一半。
更新日期:2020-09-20
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