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Hyperplane arrangements and Stopping times

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Consider a real hyperplane arrangement and let C denote the collection of the occuring chambers. Bidigare, Hanlon and Rockmore introduced a Markov chain on C which is a generalization of some card shuffling models used in computer science, biology and card games: the famous Tsetlin library used in dynamic file maintenance and cache maintenance and the riffle shuffles are two important examples of hyperplane walks. I introduce a strong stationary argument for this Markov chain, which provides explicit bounds for the separation distance. I will try to explain both the geometric and the probabilistic techniques used in the problem.

This talk is part of the Probability series.

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