We introduce a new notion of “regularity structure” that provides an algebraic framework
allowing to describe functions and/or distributions via a kind of “jet” or local Taylor expansion …

Peter K. Friz Martin Hairer With an Introduction to Regularity Structures Second Edition
Page 1 Universitext Peter K. Friz Martin Hairer A Course on Rough Paths With an …

Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …

We give a systematic description of a canonical renormalisation procedure of stochastic
PDEs containing nonlinearities involving generalised functions. This theory is based on the …

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 …

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 …

The formalism recently introduced in [BHZ19] allows one to assign a regularity structure, as
well as a corresponding “renormalisation group”, to any subcritical system of semilinear …

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 …