Local vs Non-Local Poincar\'e Inequalities and Quantitative Exponential Concentration

Stochastics Seminar
Thursday, April 4, 2024 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006
Christian Houdré – Georgia Institute of Technology
Cheng Mao

Weighted Poincar\'e inequalities known for various laws such as the exponential or Cauchy ones are shown to follow from the "usual"  Poincar\'e inequality involving the non-local gradient.  A key ingredient in showing so is a covariance representation and Hardy's inequality.  

The framework under study is quite general and comprises infinitely divisible laws as well as some log-concave ones.  This same covariance representation is then used to obtain quantitative concentration inequalities of exponential type, recovering in particular the Gaussian results.  

Joint Work with Benjamin Arras.