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 prove an a priori bound for solutions of the dynamic equation. This bound provides a
control on solutions on a compact space‐time set only in terms of the realisation of the noise …

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 obtain a generalisation of the Stroock–Varadhan support theorem for a large class of
systems of subcritical singular stochastic partial differential equations driven by a noise that …

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 …

We study Gibbs measures with log-correlated base Gaussian fields on the $ d $-
dimensional torus. In the defocusing case, the construction of such Gibbs measures follows …

We construct the $\Phi^ 4_3 $ measure on an arbitrary 3-dimensional compact Riemannian
manifold without boundary as an invariant probability measure of a singular stochastic …

We show a priori bounds for solutions to $(\partial_t-\Delta) u=\sigma (u)\xi $ in finite volume
in the framework of Hairer's Regularity Structures [Invent Math 198: 269--504, 2014]. We …

We study the hyperbolic $\Phi^{k+ 1} _2 $-model on the plane. By establishing coming down
from infinity for the associated stochastic nonlinear heat equation (SNLH) on the plane, we …

We consider the problem of ergodicity for the $ P (\Phi) _2 $ measure of quantum field theory
under the flow of the singular stochastic (damped) wave equation $ u_ {tt}+ u_t+(1-\Delta) …