Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium Mikaela Iacobelli University of Rome, Sapienza Title: A gradient flow approach to quantization of measures Abstract: The problem of quantization of a d-dimension probability distribution by discrete probabilities with a given number of points can be stated as follows: given a probability density $\rho$, approximate it in the Wasserstein metric by a convex combination of a finite number N of Dirac masses. In a recent paper in collaboration with E. Caglioti and F. Golse we studied a gradient flow approach to this problem in one dimension. By embedding the problem in $L^2$, we find a continuous version of it that corresponds to the limit as the number of particles tends to infinity. Under some suitable regularity assumptions on the density, we prove uniform stability and quantitative convergence result for the discrete and continuous dynamics.Recording: http://mm.math.cmu.edu/recordings/cna/MikaelaIacobelli_small.mp4Date: Tuesday, April 5, 2016Time: 1:30 pmLocation: Wean Hall 7218Submitted by:  Gautam Iyer