We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional
cubic wave equation, which is also known as the hyperbolic Φ 3 4-model. This result is the …

(Due to the limit on the number of characters for an abstract set by arxiv, the full abstract can
not be displayed here. See the abstract in the paper.) We study the construction of the $\Phi …

Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity
II: Dynamics Page 1 © 2023 European Mathematical Society Published by EMS Press and …

We consider the Gibbs measure for the focusing nonlinear Schr\" odinger equation on the
one-dimensional torus $\mathbb T $, that was introduced in a seminal paper by Lebowitz …

We construct the Φ 3 4 measure on a periodic three dimensional box as an absolutely
continuous perturbation of a random translation of the Gaussian free field. The shifted …

We study the construction of invariant measures associated with higher order conservation
laws of the intermediate long wave equation (ILW) and their convergence properties in the …

In this paper, we consider the defocusing Hartree nonlinear Schrödinger equations on T 3
with real-valued and even potential V and Fourier multiplier decaying such as| k|− β. By …

We study the stochastic cubic nonlinear wave equation (SNLW) with an additive noise on
the three-dimensional torus T 3. In particular, we prove local well-posedness of the …

We prove quasi-invariance of Gaussian measures supported on Sobolev spaces under the
dynamics of the three-dimensional defocusing cubic nonlinear wave equation. As in …

Abstract Lebowitz, Rose, and Speer (1988) initiated the study of focusing Gibbs measures,
which was continued by Brydges and Slade (1996), Bourgain (1997, 1999), and Carlen …