Random Walk and Hyperplane Arrangements
نویسندگان
چکیده
Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuuing schemes used in computer science, biology, and card games. It also includes random walks on zonotopes and zonotopal tilings. We nd the stationary distributions of these Markov chains, give good bounds on the rate of convergence to stationarity, and prove that the transition matrices are diagonalizable. The results are extended to oriented matroids.
منابع مشابه
Descent algebras, hyperplane arrangements, and shuffling cards. To appear
This note establishes a connection between Solomon’s descent algebras and the theory of hyperplane arrangements. It is shown that card-shuffling measures on Coxeter groups, originally defined in terms of descent algebras, have an elegant combinatorial description in terms of random walk on the chambers of hyperplane arrangements. As a corollary, a positivity conjecture of Fulman is proved.
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تاریخ انتشار 2007