# Analysis Seminar

## Gibbs Measures with Log-Correlated Gaussian Fields and its Invariance under Hamiltonian PDE

Kihoon Seong, Korea Advanced Institute of Science and Technology

Friday, February 11th, 2022
10:00 AM - 11:00 AM
Zoom ID 783 353 8838

We study the Gibbs measure with log-correlated base Gaussian fields on the d-dimensional torus. When $$d = 2$$, the Gibbs measure corresponds to the well-studied $$\Phi^k_2$$-measure in constructive quantum field theory. We first discuss the (non-)construction of the focusing Gibbs measure. As a Hamiltonian PDE system corresponding to the Gibbs measure, we consider the Zakharov-Yukawa system (Schr¨odinger-wave system with a Zakharov-type coupling) on the two-dimensional torus. We then present a phase transition and invariance of the Gibbs measure under the flow. This is based on joint work with Tadahiro Oh (University of Edinburgh) and Leonardo Tolomeo (University of Bonn).

Event contact: dan dot geba at rochester dot edu