  The starting point is the known fact that some much-studied random walks on
permutations, such as the Tsetlin library, arise from walks on real hyperplane
arrangements. This paper explores similar walks on complex hyperplane
arrangements. This is achieved by involving certain cell complexes naturally
associated with the arrangement. In a particular case this leads to walks on
libraries with several shelves.
  We also show that interval greedoids give rise to random walks belonging to
the same general family. Members of this family of Markov chains, based on
certain semigroups, have the property that all eigenvalues of the transition
matrices are non-negative real and given by a simple combinatorial formula.
  Background material needed for understanding the walks is reviewed in rather
great detail.

Combinatorics;Probability