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Monthly Archives: March 2013
Convex cones and the Hilbert metric
Having spent some time discussing spectral methods and coupling techniques as tools for studying the statistical properties of dynamical systems, we turn now to a third approach, based on convex cones and the Hilbert metric. This post is based on … Continue reading
Spectral methods 3 – central limit theorem
With the previous post on convergence of random variables, the law of large numbers, and Birkhoff’s ergodic theorem as background, we return to the spectral methods discussed in the first two posts in this series. This post is based on … Continue reading
Laws of large numbers and Birkhoff’s ergodic theorem
In preparation for the next post on the central limit theorem, it’s worth recalling the fundamental results on convergence of the average of a sequence of random variables: the law of large numbers (both weak and strong), and its strengthening … Continue reading
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