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 present a new construction of the Euclidean Φ^ 4 Φ 4 quantum field theory on R^ 3 R 3
based on PDE arguments. More precisely, we consider an approximation of the stochastic …

We introduce an explicit description of the Φ 3 4 measure on a bounded domain. Our
starting point is the interpretation of its Laplace transform as the value function of a …

We define a natural state space and Markov process associated to the stochastic Yang–Mills
heat flow in two dimensions. To accomplish this we first introduce a space of distributional …

We prove the existence of global solutions to singular SPDEs on R^\rm d R d with cubic
nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions …

(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can
not be displayed here. See the abstract in the paper.) We study the construction of the $\Phi …

We carry out the construction of some ill-posed multiplicative stochastic heat equations on
unbounded domains. The two main equations our result covers are the parabolic Anderson …

We establish that global-in-time existence and non-uniqueness of probabilistically strong
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …

We study global-in-time dynamics of the stochastic nonlinear wave equations (SNLW) with
an additive space-time white noise forcing, posed on the two-dimensional torus. Our goal in …