A Family of Random Walks on the Complement of a Hyperplane Arrangement

Phil Hanlon

University of Michigan

Feb 11, 4:15pm


Let A be a collection of hyperplanes in a Euclidean space.  This talk
concerns a family of random walks on the regions of A, i.e., on the
connected components left when the hyperplanes are removed from the
Euclidean space.  These random walks, which are called BHR shuffles, have
applications to dynamic file maintenance, modeling of changes to genetic
material, as well as to various abstract mathematical problems.  We will
discuss applications as well as properties of these random walks. In
particular, we will give a complete spectral resolution of the transition
matrices and use that information to bound convergence rates.  We will
discuss results about the stable distribution.

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