Gaussian noise stability
Given two correlated Gaussian vectors, X and Y,
the noise stability of
a set A is the probability that both X and Y fall in A. In 1985, C.
Borell proved that half-spaces maximize the noise stability among all
sets of a given Gaussian measure. We will give a new, and simpler,
proof of this fact, along with some extensions and applications.
Specifically, we will discuss hitting times for the Ornstein-Uhlenbeck
process, and a noisy Gaussian analogue of the "double bubble" problem.