Structure preservation via the Wasserstein distance (joint work with D. Bartl).

Thumbnail

Event details

Date 12.05.2023
Hour 15:1516:15
Speaker Shahar Mendelson (Australian National University)
 
Location
Category Conferences - Seminars
Event Language English

 Consider an isotropic measure \mu on R^d (i.e., centred and whose covariance is the identity) and let X_1,...,X_m be independent, selected according to \mu. If \Gamma=m^{-1/2} \sum_{i=1}^m <X_i,->e_i is the random operator whose rows are X_i/\sqrt{m}, how does the random set \Gamma S^{d-1} typically look like? For example, if the extremal singular values of \Gamma are close to 1, then \Gamma S^{d-1} is "well approximated" by a d-dimensional section of S^{m-1} and vice-versa. But is it possible to give a more accurate description of that set?
I will show that under minimal assumptions on \mu, with high probability and uniformly in t \in S^{d-1}, each vector \Gamma t  inherits the structure of the one-dimensional marginal <X,t> in a strong sense. 

If time permits I will also outline what happens when considering an arbitrary subset of S^{d-1} rather than the entire sphere. 
 

Practical information

  • Expert
  • Free

Organizer

  • Chizat Lénaïc Ged François

Share