高维管中的随机反射
Random reflections in a high dimensional tube
摘要：
本文研究了光线在$n$维半无限管中的反射问题，其中$n\geq 3$由朗伯材料制成。光源远离出口放置，并且假设光线反射，使得反射光线的方向分布具有与与法向量的角度的余弦成比例的密度。我们提出了新的结果，从管的出口分布，和推广的一些定理，从早期的文章，其中的尺寸被限制在$n=2$和$3$。
英文摘要：
We consider light ray reflections in $n$-dimensional semi-infinite tube, for $n\geq 3$, made of Lambertian material. The source of light is placed far away from the exit, and the light ray is assumed to reflect so that the distribution of the direction of the reflected light ray has the density proportional to the cosine of the angle with the normal vector. We present new results on the exit distribution from the tube, and generalizations of some theorems from an earlier article, where the dimension was limited to $n=2$ and $3$.
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