[YPNG] YPNG, Friday 22 Sept 2017 at 11:00 in 24HH classroom

[David Pollard]

Folks,

This week David P will describe
a beautiful argument of Chatterjee to prove the Fernique inequality: if  $(X_1,\dots, X_n)$ 
and $(Y_1,\dots, Y_n)$ 
are both distributed multivariate normal with $\PP X_i = \PP Y_i$  for each $i$ and
$
\var (X_I-X_j) \le \var(Y_i-Y_j)
$
for all $i$ and  $j$  then  $\mathbb P \max_i X_i \le \mathbb P \max_i Y_i $.

Motivation, background, and intuition included. All you need to know is some elementary
facts about the multivariate normal