Restricted hypercontractivity on the Poisson space
2019-07-09 10:08:56

We show that the Ornstein-Uhlenbeck semigroup associated with a general Poisson random measure is hypercontractive, whenever it is restricted to non-increasing mappings on configuration spaces. We deduce from this result some versions of Talagrand's L 1 -L 2 inequality for increasing and concave mappings, and we build examples showing that such an estimate represents a strict improvement of the classical Poincaré inequality. We complement our finding with several results of independent interest, such as gradient estimates. Jiont with Ivan Nourdin, Giovanni Peccati.