Wednesday, July 18, 2018 - 16:45 in V3-201
Metastable Markov chains, trace process and spectral theory
A talk in the Bielefeld Stochastic Afternoon series by
Nils Berglund from Université d'Orléans
| Abstract: |
I will consider discrete-time Markov chains, either in discrete or in continuous space, which are metastable in the sense that they spend long time spans in relatively small subsets of space. These chains are not assumed to be reversible. The trace process associated with a subset $A$ of space is the Markov chain monitored only when staying in $A$. Together with related Laplace transforms, this process turns out to be extremely useful to uncover the metastable dynamics of the chain, compute convergence rates to equilibrium, obtain spectral information, and prove results on approximation by Markov chains with fewer states. I will illustrate this approach on a number of simple examples.
Joint work with Manon Baudel (CERMICS, Ecole des Ponts).
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