Random Reflections in a High-Dimensional Tube

Krzysztof Burdzy () and Tvrtko Tadić ()
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Krzysztof Burdzy: University of Washington
Tvrtko Tadić: University of Zagreb

Journal of Theoretical Probability, 2018, vol. 31, issue 1, 466-493

Abstract: Abstract We consider light ray reflections in a d-dimensional semi-infinite tube, for $$d\ge 3$$ d ≥ 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 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 the cases $$d=2$$ d = 2 and $$d=3$$ d = 3 .

Keywords: Random reflections; Stopped random walks; Tail of the arccosine distribution; Undershoot; Overshoot; 60G50; 60K05; 37D50; 37H99 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-016-0703-7

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