engleski

Random Reflections and Stopped Random Walks

We study the behavior of a random reflection model (introduced by Comets et al.) in the setting of a semi-infinite tube. It turns out that this model is governed by a special case of a stopped random walk. We try to describe the behavior of the light rays exiting the tube when the source of light is far away from the exit. Using the results obtained by Doney, Erickson and Rogozin we find many explicit estimates about the limiting behavior of a symmetric random walk, its ladder variable process, the minimal solution of the Wiener-Hopf equation and the undershoot and overshoot. This in the end produces nice results about the luminosity of the points in the tube. Joint work in progress with Krzysztof Burdzy.

random reflections; stopped random walks

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