Many seemingly disparate Markov chains are unified when viewed as random
walks on the set of chambers of a hyperplane arrangement. These include the
Tsetlin library of theoretical computer science and various shuffling schemes.
If only selected features of the chains are of interest, then the mixing times
may change. We study the behavior of hyperplane walks, viewed on a
subarrangement of a hyperplane arrangement. These include many new examples,
for instance a random walk on the set of acyclic orientations of a graph. All
such walks can be treated in a uniform fashion, yielding diagonalizable
matrices with known eigenvalues, stationary distribution and good rates of
convergence to stationarity.Comment: Final version; Section 4 has been split into two section