2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101151We 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.New corrected version; 22 pages; 1 figure; New result added: stretched-exponential inequalityProbabilityMathematical Physicstext