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SUMMARY:Structure preservation via the Wasserstein distance (joint work wi
 th D. Bartl).
DTSTART:20230512T151500
DTEND:20230512T161500
DTSTAMP:20260512T045950Z
UID:29c84ccfcc4283612563ddd982a88420d9bf51d3ec9099a7e12fdee9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Shahar Mendelson (Australian National University)\n \n\n Con
 sider an isotropic measure \\mu on R^d (i.e.\, centred and whose covarianc
 e is the identity) and let X_1\,...\,X_m be independent\, selected accordi
 ng to \\mu. If \\Gamma=m^{-1/2} \\sum_{i=1}^m <X_i\,->e_i is the random op
 erator 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 giv
 e a more accurate description of that set?\nI 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. \n\nIf time permits I will also outli
 ne what happens when considering an arbitrary subset of S^{d-1} rather tha
 n the entire sphere. \n 
LOCATION:CM 1 5 https://plan.epfl.ch/?room==CM%201%205
STATUS:CONFIRMED
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