Personal webpage of Valentina Kiritchenko

Faculty of Mathematics

January 10, Wednesday, 15:30, room 211

shinymath, · Categories: Без рубрики

Dmitry Korshunov

Concentration of measure phenomenon 

Dvoretzky-Milman theorem says that very high dimensional symmetric
convex bodies inevitably have sections that are nearly ellipsoids.
Stated initially by Grothendieck as a conjecture in the asymptotic
theory of Banach spaces it was proved by Dvoretzky in 1961. But it was
only after Milman’s simple proof via isoperimetric inequality and
concentration of measure phenomenon (this is exactly the effect
responsible for a thick skin of a high-dimensional orange) that many
connections of this question with as diverse fields as Riemannian
geometry, functional analysis, combinatorics and computer science
became apparent.
This story can be viewed as a geometric manifestation of both the law
of large numbers of Probability theory and Ramsey theory of
Combinatorics. We shall discuss Milman’s proof of Dvoretzky-Milman