Gaussian lower bounds for the density via Malliavin calculus

In this paper, based on a known formula, we use a simple idea to get a new representation for the density of Malliavin differentiable random variables. This new representation is particularly useful for finding lower bounds for the density.Comment: To appear in Comptes Rendus Mathematique, 10 page

An improved bound for the Gaussian concentration inequality

In this note, we provide an improved bound for the Gaussian concentration inequality. Our proof is short and bases on the integration-by-parts formula for the gaussian measure.Comment: 4 page