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-
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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