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). |
5. | Publisher | Organizing agency, location | |
6. | Contributor | Sponsor(s) | |
7. | Date | (YYYY-MM-DD) | 2014-08-11 |
8. | Type | Status & genre | Peer-reviewed Article |
8. | Type | Type | |
9. | Format | File format | |
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 |
14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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