Concentration inequalities for random fields via coupling
Abstract
We present a new and simple approach to concentration inequalities for functions around their expectation with respect to nonproduct 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 stretchedexponential concentration inequalities. Our abstract results apply to Gibbs random fields, in particular to the lowtemperature Ising model which is a concrete example of nonuniformity of the coupling.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2005
 arXiv:
 arXiv:math/0503483
 Bibcode:
 2005math......3483C
 Keywords:

 Mathematics  Probability;
 Mathematics  Mathematical Physics;
 Mathematical Physics
 EPrint:
 New corrected version