Title: Random reflections in a high dimensional tube Show Chinese title

Title: 高维管道中的随机反射

Abstract: 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 $3$. Show Chinese abstract

Abstract: 我们考虑在$n$维半无限管中光束的反射，对于$n\geq 3$，该管由朗伯材料制成。光源放置在远离出口的地方，并且假设光束反射使得反射光束方向的分布密度与法向量夹角的余弦成比例。我们提出了关于从管中出口分布的新结果，并推广了早期文章中的一些定理，其中维度被限制为$n=2$和$3$。