Tag Archives: Markov chains

The Perron-Frobenius theorem and the Hilbert metric

In the last post, we introduced basic properties of convex cones and the Hilbert metric. In this post, we look at how these tools can be used to obtain an explicit estimate on the rate of convergence in the Perron–Frobenius … Continue reading

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Markov chains and mixing times (part 3)

The previous post introduced the idea of coupling for Markov chains as a method for estimating mixing times. Here we mention a particular example of a coupling that is often useful — this is the classical coupling, or Doeblin coupling, … Continue reading

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Markov chains and mixing times (part 2 – coupling)

This week’s post continues last week’s discussion of Markov chains and mixing times, and introduces the idea of coupling as a method for estimating mixing times. We remark that some nice notes on the subject of coupling (and others) can … Continue reading

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Markov chains and mixing times

Our seminar series is taking a hiatus from spectral methods for a couple weeks — these will return eventually, but in the meantime we’ll spend some time with the idea of coupling as a method for deriving statistical properties. In … Continue reading

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