Concentration inequalities for random fields via coupling
Probability
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
We present a new and simple approach to concentration inequalities for functions around their expectation with respect to non-product measures, i.e., for dependent random variables. Our method is based on coupling ideas and does not use information inequalities. When one has a uniform control on the coupling, this leads to exponential concentration inequalities. When such a uniform control is no more possible, this leads to polynomial or stretched-exponential concentration inequalities. Our abstract results apply to Gibbs random fields, in particular to the low-temperature Ising model which is a concrete example of non-uniformity of the coupling.
Cite
@article{arxiv.math/0503483,
title = {Concentration inequalities for random fields via coupling},
author = {J. -R. Chazottes and P. Collet and C. Kuelske and F. Redig},
journal= {arXiv preprint arXiv:math/0503483},
year = {2007}
}
Comments
New corrected version; 22 pages; 1 figure; New result added: stretched-exponential inequality