INVARIANT GIBBS MEASURES AND HAMILTONIAN PDES
SAMANTHA XU
Abstract
Liouville’s Theorem says that the flow of a Hamiltonian ODE preserves Lebesgue measure, and
a corresponding Gibbs measure as well. This notion can be generalized to infinite dimensional
systems for various Hamiltonian PDEs. In this talk, we will discuss the role of randomization on
initial datum, methods of constructing an invariant Gibbs measure, and some recent results.
1