Topics in Markov chains: mixing and escape rate

2015/06/16 by Júlia Komjáthy, Julia Komjathy, Yuval Peres +2 · 1 citation
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Computer science #Econometrics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Markov chain #Mathematical economics #Mathematics #Mixing (physics) #Physics #Probability (math.PR) #Quantum mechanics #Statistical physics #Statistics #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1506.04850

published in arXiv (Cornell University) (Cornell University) · 28 pages, 1 figure

arxiv created 2015/06/16 · openalex publication_date 2015/06/16 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Markov chains revisited
• Finite Markov chains and Monte-Carlo Methods: An Undergraduate Introduction
• Empirical and Instance-Dependent Estimation of Markov Chain and Mixing Time
• Mixing times of Markov chains on a cycle with additional long range connections
• Mixing Times and Hitting Times for General Markov Processes