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 …

We develop a martingale approach for a class of singular stochastic PDEs of Burgers type
(including fractional and multi-component Burgers equations) by constructing a domain for …

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 establish a surface order large deviation estimate for the magnetisation of low
temperature ϕ 3 4. As a byproduct, we obtain a decay of spectral gap for its Glauber …

The continuum $\varphi^ 4_2 $ and $\varphi^ 4_3 $ measures are shown to satisfy a log-
Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that …

In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow
is symmetric with respect to a measure induced by Liouville conformal field theory. Using the …

I will review the setting and some of the recent results in the field of singular stochastic
partial differential equations (SSPDEs). Since Hairer's invention of regularity structures this …

We apply Malliavin calculus to the Φ^4_3 equation on the torus and prove existence of
densities for the solution of the equation evaluated at regular enough test functions. We work …

We consider the modified Surface Quasi-Geostrophic (mSQG) equation on the 2D torus T 2,
perturbed by multiplicative transport noise. The equation admits the white noise measure on …

We prove that there exists a diffusion process whose invariant measure is the three
dimensional polymer measure $\nu_\lambda $ for small $\lambda> 0$. We follow in part a …