Long-term concentration of measure and cut-off
| Autor: | Barbour, Andrew, Brightwell, Graham, Luczak, Malwina |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 60 pages; substantially revised in response to referee comments; accepted for publication in Stochastic Processes and Applications |
| Databáze: | arXiv |
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