2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71237Using Talagrand's concentration inequality on the discrete cube {0,1}^m we show that given a real-valued function Z(x)on {0,1}^m that satisfies certain monotonicity conditions one can control the deviations of Z(x) above its median by a local Lipschitz norm of Z(x) at the point x. As one application, we give a simple proof of a nearly optimal deviation inequality for the number of k-cycles in a random graph.11 pages, 1 figureProbabilityCombinatorics60E15text