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Markov chains and mixing times

The course treats the theory for discrete-time Markov chains.

Central to the course are stationary distributions and convergence towards the stationary distribution. In particular, focus will lie on so-called mixing times, i.e. the time is takes for a Markov chain to approach the stationary distribution, and methods for estimating these. The theory will be illustrated through applications to card shufflings, random walks, statistical physics and/orgenetics. One or more of the following topics will be treated further in some depth: random walks and electrical networks, algorithmic methods such as MCMC-algorithms, and genetic mutations.