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 …

Yang–Mills (YM) theory plays an important role in the description of force-carrying particles
in the standard model. An important unsolved problem in mathematics is to show that YM …

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 …

We define a state space and a Markov process associated to the stochastic quantisation
equation of Yang–Mills–Higgs (YMH) theories. The state space S is a nonlinear metric …

We provide a relatively compact proof of the BPHZ theorem for regularity structures of
decorated trees in the case where the driving noise satisfies a suitable spectral gap …

We provide an algebraic framework to describe renormalization in regularity structures
based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is …

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 introduce a numerical framework for dispersive equations embedding their underlying
resonance structure into the discretisation. This will allow us to resolve the nonlinear …

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 …