Abstract for the talk on 09.06.2022 (17:00 h)

Webinar “Analysis, Quantum Fields, and Probability”

Bjoern Bringmann (IAS Princeton)
Invariant Gibbs measures for the three-dimensional cubic nonlinear wave equation

In this talk, we prove the invariance of the Gibbs measure for the three-dimensional

cubic nonlinear wave equation, which is also known as the hyperbolic Φ4 3-

model. This result is

the hyperbolic counterpart to seminal works on the parabolic Φ4 3-

model by Hairer ’14 and Hairer-

Matetski ’18.

In the first half of this talk, we illustrate Gibbs measures in the context of Hamiltonian ODEs,

which serve as toy-models. We also connect our theorem with classical and recent developments

in constructive QFT, dispersive PDEs, and stochastic PDEs.

In the second half of this talk, we give a non-technical overview of the proof. As part of this

overview, we first introduce a caloric representation of the Gibbs measure, which leads to an inter-

play of both parabolic and hyperbolic theories. Then, we briefly discuss the local dynamics of the

cubic nonlinear wave equation, focusing on a hidden cancellation between sextic stochastic objects.

This is joint work with Y. Deng, A. Nahmod, and H. Yue.

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