Abstract
An inequality of Marton (Ann. Probab. 24 (1996) 857–866) shows that the joint distribution of a Markov chain with uniformly contracting transition kernels exhibits concentration. We generalize this inequality to Markov chains indexed by trees.
Une inégalité de Marton (Ann. Probab. 24 (1996) 857–866) montre que la loi jointe d’une chaîne de Markov avec des noyaux de transition uniformément contractants présente un phénomène de concentration. Nous généralisons cette inégalité aux chaînes de Markov indexées par des arbres.
Funding Statement
This material is based upon work supported by the National Science Foundation under Grant No. DMS 1344970.
Acknowledgements
The author would like to thank Tim Austin and Georg Menz for many helpful discussions and feedback on earlier versions of the paper, and Aryeh Kontorovich and anonymous reviewers for providing feedback on preprints.
Citation
Christopher Shriver. "Concentration of Markov chains indexed by trees." Ann. Inst. H. Poincaré Probab. Statist. 58 (3) 1701 - 1711, August 2022. https://doi.org/10.1214/21-AIHP1224
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