

Abstract for the talk on 23.10.2018 (16:45 h)
Oberseminar ANALYSIS - PROBABILITYMax Fathi (CNRS & Université Paul Sabatier)
Stability for the Bakry-Emery theorem
The Bakry-Emery theorem states that if a probability measure is in some sense more
log-concave than the standard Gaussian measure, then certain functional
inequalities (such as the Poincare inequality and the logarithmic
Sobolev inequality) hold, with better constants than for the associated
Gaussian inequalities. I will show how we can combine Stein's method and
simple variational arguments to show that if the Bakry-Emery bound is
almost sharp for a given measure, then that measure must almost split
off a Gaussian factor, with explicit quantitative bounds. Joint work with Thomas Courtade.