Concentration inequalities for random fields via coupling
Chazottes, J. -R. ; Collet, P. ; Kuelske, C. ; Redig, F.
arXiv, 0503483 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-03-23
Classification:  Mathematics - Probability,  Mathematical Physics 
@article{0503483,
     author = {Chazottes, J. -R. and Collet, P. and Kuelske, C. and Redig, F.},
     title = {Concentration inequalities for random fields via coupling},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0503483}
}

Chazottes, J. -R.; Collet, P.; Kuelske, C.; Redig, F. Concentration inequalities for random fields via coupling. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0503483/