Stefan Steinerberger : Wasserstein Distance as a Tool in Analysis
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.
- Category: Applied Math and Analysis
- Duration: 01:14:48
- Date: April 24, 2019 at 11:55 AM
- Views: 135
- Tags: seminar, Applied Math And Analysis Seminar
0 Comments