Recurrence properties of planar Lorentz process
Recurrence properties of planar Lorentz process
复制标题
平面洛伦兹过程的递归性质
DOI：
10.1215/00127094-2008-006
复制
发表时间：
2008
影响因子：
2.5
通讯作者：
Tamás Varjú
中科院分区：
文献类型：
--
作者：
D. Dolgopyat;D. Szász;Tamás Varjú
研究了具有周期性散射体的平面有限视界Lorentz过程的首回、首中时、局部时和首交时。它们的渐近行为类似于2-D简单对称随机游动的等量的渐近行为。Darling-Kac，1957年和ErdőS-泰勒，1960年的经典结果)。此外，还描述了Lorentz过程的第一次碰撞和第一次相交中的相位的渐近分布。所得结果也推广到线性洛伦兹过程的准一维模型。科目分类：37D50台球，60F05弱定理
First return and first hitting times, local times and first intersection times are studied for planar finite horizon Lorentz processes with a periodic configuration of scatterers. Their asymptotic behavior is analogous to the asymptotic behavior of the same quantities for the 2-d simple symmetric random walk (cf. classical results of Darling-Kac, 1957 and of Erdős-Taylor, 1960). Moreover, asymptotical distributions for phases in first hittings and in first intersections of Lorentz processes are also described. The results are also extended to the quasi-one-dimensional model of the linear Lorentz process. Subject classification: 37D50 billiards, 60F05 weak theorems