Functions of random walks on hyperplane arrangements

Details Functions of random walks on hyperplane arrangements Functions of random walks on hyperplane arrangements

2009-12-09

arxiv.org/abs/0912.1686v3

Mathematics

Combinatorics

Final version; Section 4 has been split into two sections

Scientific paper

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.

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