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Random Reflections in a High-Dimensional Tube

Author

Listed:
  • Krzysztof Burdzy

    (University of Washington)

  • Tvrtko Tadić

    (University of Zagreb
    Microsoft Corporation (City Center Plaza Bellevue))

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 .

Suggested Citation

  • Krzysztof Burdzy & Tvrtko Tadić, 2018. "Random Reflections in a High-Dimensional Tube," Journal of Theoretical Probability, Springer, vol. 31(1), pages 466-493, March.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:1:d:10.1007_s10959-016-0703-7
    DOI: 10.1007/s10959-016-0703-7
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    References listed on IDEAS

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    1. Veraverbeke, N., 1977. "Asymptotic behaviour of Wiener-Hopf factors of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 27-37, February.
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