We analyze the one-dimensional periodic Kardar–Parisi–Zhang equation in the language of
paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer …

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

We prove an a priori bound for the dynamic Φ^ 4_3 Φ 3 4 model on the torus which is
independent of the initial condition. In particular, this bound rules out the possibility of finite …

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 develop a general framework for spatial discretisations of parabolic stochastic PDEs
whose solutions are provided in the framework of the theory of regularity structures and …

We give a direct construction of invariant measures and global flows for the stochastic
quantization equation to the quantum field theoretical $\Phi^ 4_3 $-model on the $3 …

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

We derive a multiscale generalisation of the Bakry‐Émery criterion for a measure to satisfy a
log‐Sobolev inequality. Our criterion relies on the control of an associated PDE well‐known …

We develop in this work a general version of paracontrolled calculus that allows to treat
analytically within this paradigm a whole class of singular partial differential equations with …

Abstract The continuum φ 2 4 φ^4_2 and φ 3 4 φ^4_3 measures are shown to satisfy a log‐
Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that …