Méthodes fonctionnelles pour des grandes déviations quasi-gaussiennes
Résumé
Some Gaussian functional inequalities have simple generalizations to some Gaussianlike cases. They allow us to establish Gaussian-like Large Deviations Principles and bounds via Gaussian concentration and shift inequalities for certain families of Boltzmann measures and laws of diffusion semigroups in short time. Beyond the results themselves, we would like to emphasize here the method and the symmetry of the arguments used for upper and lower bounds by means of the functional inequalities.