ABSTRACT

  In this talk, we first discuss the construction of invariant
Gibbs measures on the circle by Bourgain '94. Then, we discuss the situation
on the real line by taking larger and larger periods. Previously, Bourgain '00
considered this problem and proved uniqueness of solutions to (sub-)cubic NLS
with the Gibbs measure as initial data. By viewing such initial data as a
diffusion process in x, we extend this result to (sub-)quintic NLS.