Intrinsic dimensional functional inequalities on model spaces

We shall present various “intrinsic dimensional” versions of classical functional inequalities. In the first part of the talk we will discuss the effect of scaling on Euclidean inequalities (log-Sobolev, Beckner, Gagliardo-Nirenberg). In the second part we will explain a stochastic approach leading to refined log-Sobolev inequalities on the sphere and the hyperbolic space.