Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics
Bjoern Bringmann
Abstract
In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences.
Topics & Concepts
MathematicsGibbs measureMathematical analysisGaussianSingularityInvariant measureNonlinear systemMeasure (data warehouse)Statistical physicsQuantum mechanicsPhysicsErgodic theoryComputer scienceDatabaseStatistical Mechanics and EntropyOceanographic and Atmospheric ProcessesOcean Waves and Remote Sensing