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.
Publié le : 1998-10-14
Classification:
RAndom walk,
Markov chain,
hyperplane arrangement,
zonotope,
eigenvalues,
diagonalizable matrix,
oriented matroid,
60J10,
52B30
@article{1022855884,
author = {Brown, Kenneth S. and Diaconis, Persi},
title = {Random walks and hyperplane arrangements},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1813-1854},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855884}
}
Brown, Kenneth S.; Diaconis, Persi. Random walks and hyperplane arrangements. Ann. Probab., Tome 26 (1998) no. 1, pp. 1813-1854. http://gdmltest.u-ga.fr/item/1022855884/