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The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems


 
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1. Title Title of document The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems
 
2. Creator Author's name, affiliation, country Daniel Paulin; National University of Singapore; Singapore
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) concentration inequalities; Stein's method; exchangeable pairs; reversible Markov chains; stochastic travelling salesman problem; Steiner tree; sampling without replacement; Dobrushin condition; exponential random graph
 
3. Subject Subject classification 60E15; 82B44
 
4. Description 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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7. Date (YYYY-MM-DD) 2014-08-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3261
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3261
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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