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Tag Archives: spectral methods
The PerronFrobenius 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
Posted in theorems
Tagged Hilbert metric, Markov chains, PerronFrobenius, spectral methods
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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
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
Posted in examples, statistical laws
Tagged decay of correlations, Markov chains, PerronFrobenius, spectral methods
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Spectral methods in dynamics (part 2)
This is a continuation of the last post, which were notes from the first in a series of talks at the Houston dynamics seminar on spectral methods for transfer operators as tools to establish statistical properties of dynamical systems. This … Continue reading
Posted in ergodic theory, examples, statistical laws
Tagged interval maps, physical measures, spectral methods, transfer operator
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Spectral methods in dynamics
In the dynamics seminar here at Houston, we’re beginning a series of expository talks on statistical properties of dynamical systems. This week’s talk was given by Andrew Török and introduces some of the spectral methods for transfer operators that prove … Continue reading