Open Access
2015 A method to derive concentration of measure bounds on Markov chains
Stephen Ng, Meg Walters
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Electron. Commun. Probab. 20: 1-13 (2015). DOI: 10.1214/ECP.v20-3817


We explore a method introduced by Chatterjee and Ledoux in a paper on eigenvalues of principle submatrices. The method provides a tool to prove concentration of measure in cases where there is a Markov chain meeting certain conditions, and where the spectral gap of the chain is known. We provide several additional applications of this method. These applications include results on operator compressions using the Kac walk on $SO(n)$ and a Kac walk coupled to a thermostat, and a concentration of measure result for the length of the longest increasing subsequence of a random walk distributed under the invariant measure for the asymmetric exclusion process.


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Stephen Ng. Meg Walters. "A method to derive concentration of measure bounds on Markov chains." Electron. Commun. Probab. 20 1 - 13, 2015.


Accepted: 20 December 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1334.60147
MathSciNet: MR3438740
Digital Object Identifier: 10.1214/ECP.v20-3817

Primary: Probability
Secondary: Mathematical Physics

Keywords: concentration of measure , Markov chains , spectral gap

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