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2014 The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems
Daniel Paulin
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Electron. J. Probab. 19(none): 1-34 (2014). DOI: 10.1214/EJP.v19-3261

Abstract

We prove concentration inequalities for general functions of weakly dependent random variables satisfying the Dobrushin condition. In particular, we show Talagrand's convex distance inequality for this type of dependence. We apply our bounds to a version of the stochastic salesman problem, the Steiner tree problem, the total magnetisation of the Curie-Weiss model with external field, and exponential random graph models. Our proof uses the exchangeable pair method for proving concentration inequalities introduced by Chatterjee (2005). Another key ingredient of the proof is a subclass of $(a,b)$-self-bounding functions, introduced by Boucheron, Lugosi and Massart (2009).

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Daniel Paulin. "The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems." Electron. J. Probab. 19 1 - 34, 2014. https://doi.org/10.1214/EJP.v19-3261

Information

Accepted: 11 August 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1330.60039
MathSciNet: MR3248197
Digital Object Identifier: 10.1214/EJP.v19-3261

Subjects:
Primary: 60E15
Secondary: 82B44

JOURNAL ARTICLE
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Vol.19 • 2014
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