Orateur
Description
In this talk, we address the stability problem of the variance
Brascamp-Lieb. More precisely, if a given function almost
satisfies the equality in the BL inequality, is it true that it is close
(here in L^2) to the underlying extremal functions ?
To answer this, we will first rewrite the BL inequality as a standard Poincaré inequality but for a diffusion operator adapted to the energy in the BL inequality. We will then prove that the stability is in fact equivalent to a second order spectral gap for this operator. Moreover, using intertwining, this second order spectral gap may also be seen as a standard spectral gap but for an operator acting on gradients.
Our results will be illustrated by some new examples of stability.
This is a joint work with A. Joulin (Institut de Mathématiques de Toulouse) and J. Serres (Sorbonne Université).