Topics in Markov chains: mixing and escape rate
Julia Komjathy, Yuval Peres
TL;DR
This paper provides an overview of methods for estimating mixing times and escape rates in Markov chains, highlighting lamplighter groups and the Varopolous-Carne estimate as key tools.
Contribution
It introduces and discusses techniques for analyzing mixing and escape rates in Markov chains, with a focus on lamplighter groups and long-range estimates.
Findings
Lamplighter groups as key examples
Varopolous-Carne estimate's usefulness in both settings
Methods for estimating mixing times and escape rates
Abstract
These are the notes for the minicourse on Markov chains delivered at the Saint Petersburg Summer School, June 2012. The main emphasis is on methods for estimating mixing times (for finite chains) and escape rates (for infinite chains). Lamplighter groups are key examples in both topics and the Varopolous-Carne long range estimate is useful in both settings.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Stochastic processes and statistical mechanics · Bayesian Modeling and Causal Inference