发表机构
ESSEC; Polytechnic Institute of Paris（ESSEC高等商学院; 巴黎理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过有限体积数值实验研究平面洛伦兹镜模型的边界透射与游走几何，发现穿透分位数近似线性增长、透射概率呈指数约束、游走横向范围与出口半径成正比，并揭示了重路由对路径的缩短作用。
AI 中文摘要
我们通过有限体积数值实验研究平面洛伦兹镜模型中的边界透射与游走几何。在模拟范围内，圆柱穿透分位数随周长近似线性增长，当存在空位时，归一化分位数出现系统性向上漂移。估计的平板透射概率在测试宽度下给出了具有量化统计置信度的指数约束界。以到达远处边界为条件的平面游走，其横向范围与出口半径成正比，而其重复访问分数随镜密度强烈变化。端点标签碰撞概率显著超过一般粘合下界，尽管它们仅占观察到的同列穿越概率的一部分。最后，在重复顶点处重新路由保留了出口，同时显著缩短了采样路径。这些发现刻画了有限体积输运与游走几何，但未确定渐近标度指数或解决无限平面局域化问题。
英文摘要
We study boundary transmission and excursion geometry in the planar Lorentz mirror model through finite-volume numerical experiments. Cylinder penetration quantiles grow approximately linearly with circumference over the simulated range, with a systematic upward drift in the normalized quantiles when vacancies are present. Estimated slab-transmission probabilities yield exponential confinement bounds with quantified statistical confidence at the tested widths. Planar excursions conditioned to reach a distant boundary exhibit transverse ranges proportional to the exit radius, while their repeated-visit fractions vary strongly with mirror density. Endpoint-label collision probabilities substantially exceed a general gluing lower bound, although they account for only part of the observed same-column crossing probability. Finally, rerouting at repeated vertices preserves the exit while substantially shortening the sampled paths. These findings characterize finite-volume transport and excursion geometry without determining an asymptotic scaling exponent or resolving infinite-plane localization.
Comments15 pages
