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 …

Global well-posedness of the dynamic Phi4 modelin the plane Page 1 The Annals of Probability
2017, Vol. 45, No. 4, 2398–2476 DOI: 10.1214/16-AOP1116 © Institute of Mathematical …

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 …

Paracontrolled distributions and the 3-dimensional stochastic quantization equation Page 1
The Annals of Probability 2018, Vol. 46, No. 5, 2621–2679 https://doi.org/10.1214/17-AOP1235 …

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 study the long time behavior of the stochastic quantization equation. Extending recent
results by Mourrat and Weber (Global well-posedness of the dynamic ϕ^4 in the plane …

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 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 …

These lecture notes grew out of a series of lectures given by the second named author in
short courses in Toulouse, Matsumoto, and Darmstadt. The main aim is to explain some …