Hopf algebras and Markov ChainsAlgebra & Discrete Mathematics
|Persi Diaconis, Stanford University
|Mon, Oct 29 2012, 4:10PM
Hopf algebras are gadgets invented and studied by topologists and group theorists. In recent years, combinatorialists have found them useful in keeping track of putting together and tearing apart their natural objects. In joint work with Amy Pang and Arun Ram we have found that we can associate a Markov chain with combinatorial Hopf algebras. These specialize to riffle shuffling and Kolomogorov's model of rock breaking (among many others). The Hopf machine gives all the eigenvalues and eigenvectors.