Abstract for the talk on 23.10.2018 (16:45 h)

Oberseminar ANALYSIS - PROBABILITY

Max 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.