Open Access
October 1998 Random walks and hyperplane arrangements
Kenneth S. Brown, Persi Diaconis
Ann. Probab. 26(4): 1813-1854 (October 1998). DOI: 10.1214/aop/1022855884


Let $\mathscr{C}$ be the set of chambers of a real hyperplane arrangement. We study a random walk on $\mathscr{C}$ introduced by Bidigare, Hanlon and Rockmore. This includes various shuffling schemes used in computer science, biology and card games. It also includes random walks on zonotopes and zonotopal tilings. We find 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.


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Kenneth S. Brown. Persi Diaconis. "Random walks and hyperplane arrangements." Ann. Probab. 26 (4) 1813 - 1854, October 1998.


Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0938.60064
MathSciNet: MR1675083
Digital Object Identifier: 10.1214/aop/1022855884

Primary: 52B30 , 60J10

Keywords: diagonalizable matrix , Eigenvalues , hyperplane arrangement , Markov chain , oriented matroid , Random walk , zonotope

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 4 • October 1998
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