# Mathematics Colloquia and Seminars

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### Rates of convergence for some classes of Markov chains with polynomial eigenfunctions

**Mathematical Physics & Probability**

Speaker: | Kshitij Khare, Stanford University |

Location: | 2112 MSB |

Start time: | Wed, Sep 24 2008, 4:10PM |

In my talk I will present three families of Markov chains for which the eigenfunctions turn out to be well-known orthogonal polynomials. This knowledge can be used to come up with exact rates of convergence for these families of Markov chains. The first family of examples is two-component Gibbs samplers involving standard exponential families and their conjugate priors, the second family of examples is the multivariate normal autoregressive process and the third family of examples consists of simple models in population genetics. These are joint works with Persi Diaconis, Laurent Saloff-Coste and Hua Zhou.