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Talk

Stability for the Bakry-Emery theorem

  • Max Fathi (CNRS & Université Paul Sabatier)
A3 01 (Sophus-Lie room)

Abstract

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.

Upcoming Events of this Seminar

  • Dienstag, 11.03.25 tba with Jianfeng Lu
  • Dienstag, 11.03.25 tba with Steffen Börm
  • Dienstag, 06.05.25 tba with Ilya Chevyrev
  • Dienstag, 03.06.25 tba with Mate Gerencser