# On the structure of random coordinate projections

The Gine-Zinn symmetrization theorem shows that the suprema of natural empirical processes indexed by a class is determined by the structure of a typical coordinate projection of the class, namely, \{ (f(X_i))_{i=1}^N : f \in F\}. I will survey some results on the geometric structure of these random sets, their connection with Dvoretzky type theorems, and the way the structure exhibits various probabilistic phenomena, like the uniform law of large numbers and the central limit theorem with weak boundedness assumptions.

This talk is part of the Probability Theory and Statistics in High and Infinite Dimensions series.