Long-term concentration of measure and cut-off

Barbour, A.D., Brightwell, Graham and Luczak, Malwina J. (2022) Long-term concentration of measure and cut-off. Stochastic Processes and Their Applications, 152. 378 - 423. ISSN 0304-4149

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Abstract

We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited to establishing the cut-off phenomenon for suitable chains. We apply our discrete-time inequality to the well-studied Bernoulli–Laplace model of diffusion, and give a probabilistic proof of cut-off, recovering and improving the bounds of Diaconis and Shahshahani. We also extend the notion of cut-off to chains with an infinite state space, and illustrate this in a second example, of a two-host model of disease in continuous time. We give a third example, giving concentration results for the supermarket model, illustrating the full generality and power of our results.

Item Type:	Article
Official URL:	https://www.sciencedirect.com/journal/stochastic-p...
Additional Information:	© 2022 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	25 May 2022 09:12
Last Modified:	12 Dec 2024 03:01
URI:	http://eprints.lse.ac.uk/id/eprint/115196

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