Abstract:

The complement of a real hyperplane arrangement consists of a finite number of connected regions. A class of random walks on these regions was introduced and studied by Bidigare-Hanlon-Rockmore, Brown-Diaconis and others. Specialised to the braid arrangement it contains some well-known walks on permutations, such as random-to-top card shuffle (aka "the Tsetlin library") and inverse riffle shuffle. I will describe how there are analogous walks on the complement of complex hyperplane arrangements, using cell decompositions. For the braid arrangement this yields, among other things, a Tsetlin library with $k$ shelves.