Naslov
Random reflections in a high-dimensional tube

Autori
Burdzy, Krzysztof ; Tadić, Tvrtko

Izvornik
Journal of theoretical probability (0894-9840) 31 (2018); 466-493

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
random reflections ; stopped random walks ; tail of the arccosine distribution ; undershoot ; overshoot

Sažetak
We consider light ray reflections in $d$-dimensional semi-infinite tube, for $d\geq 3$, 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 $d=2$ and $3$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA