## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, February 20, 2018, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Anders Martinsson

## Segregating Markov chains

It is a well-known fact that a Markov chain, under some assumptions, mixes'' in the sense that it forgets its inital state'' and converges to a unique stationary distribution as time tends to infinity. In investigating the rate of this convergence, coupling arguments play a big role. One common idea is to let two copies of the Markov chain, with different starting positions, evolve dependently on each other in some clever way such that they meet up fast, and then bound their distance in distribution by this first meeting time. In this talk, we will investigate an observation by Häggström in which, by removing some standard and commonly overlooked assumptions, it is possible to couple two copies of a Markov chain to meet a.s. while not (completely) mixing. This is joint work with Timo Hirscher.

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