Date and Time:
Fridays 3:00-4:30pm in Math 528.
General Description:
This learning/reading seminar is for everyone that is interested in Stochastic Differential Equations, Diffusion processes, and the inequalities stemming from the celebrated HWI inequality of Otto and Villani such as the Talagrands inequality and the Log-Sobolov inequality. This area of mathematics connects optimal transport and geometry of probability measures with information theory and stochastic calculus.
We will first go over the Chafai-Lehec Survey (Logarithmic Sobolev Inequality Essentials) and the paper of Karaztas, Schachermayer, and Tschiderer 2022 paper (TPA) on Langevin-Smoluchowski Diffusions (email at rg3641@columbia.edu for Pdfs). The plan would be to take turns on presenting parts of the material every week and then take turns on presenting papers/ work stemming from the theory covered. This plan is subject to changes depending on the interest of attendees.
For any questions about the seminar, please email the organizer Raphael Grondin at rg3641@columbia.edu.
Tentative Schedule:
Date: Topic: Speaker:
09/18 Ornstein-Uhlenbeck (OU) Process/Semigroup, Poincare and Log-Sob. Ine., Conv. to Equilibrium and Amnesia Raphael Grondin
09/25 Poincare, Log Sobolev Inequality for the stand. gaussian. Convergence to Equilibrium and Amnesia of OU process. Raphael Grondin
If time permits: hypercontractivity and spectral gap of OU process.
10/02 Hypercontractivity, spectral gap of OU process and links with information theory. If time permits: tensorization and Chenyang Sun
links with the dimension independence of Log-Sobolev constant.
10/09 Concentration of measure, transportation inequalities. AJ LaMotta
10/16 Isoperimetric inequality for the Gaussian and link with Log-Sobolev inequality. Liam Stratford Dennehy