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

- Series
- Stochastics Seminar
- Time
- Thursday, April 4, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Christian Houdré – Georgia Institute of Technology

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.