We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear
Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that …

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 …

We present a new construction of the Euclidean Φ^ 4 Φ 4 quantum field theory on R^ 3 R 3
based on PDE arguments. More precisely, we consider an approximation of the stochastic …

We introduce the theory of random tensors, which naturally extends the method of random
averaging operators in our earlier work (Deng et al. in: Invariant Gibbs measures and global …

We define a state space and a Markov process associated to the stochastic quantisation
equation of Yang–Mills–Higgs (YMH) theories. The state space S is a nonlinear metric …

We define a natural state space and Markov process associated to the stochastic Yang–Mills
heat flow in two dimensions. To accomplish this we first introduce a space of distributional …

(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 …

This introduction surveys a renormalisation group perspective on log-Sobolev inequalities
and related properties of stochastic dynamics. We also explain the relationship of this …

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 …

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 …