We introduce an approach to study certain singular partial differential equations (PDEs)
which is based on techniques from paradifferential calculus and on ideas from the theory of …

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 …

We consider a natural class of ${\mathbf {R}}^ d $-valued one-dimensional stochastic partial
differential equations (PDEs) driven by space-time white noise that is formally invariant …

We develop a discrete version of paracontrolled distributions as a tool for deriving scaling
limits of lattice systems, and we provide a formulation of paracontrolled distributions in …

In this paper we consider the Anderson Hamiltonian with white noise potential on the box [0,
L] 2 with Dirichlet boundary conditions. We show that all of the eigenvalues divided by log L …

arXiv:2208.09352v1 [math.AP] 19 Aug 2022 Page 1 arXiv:2208.09352v1 [math.AP] 19 Aug 2022
Anderson Hamiltonian and associated Nonlinear Stochastic Wave and Schrödinger equations …

Stochastic PDEs are ubiquitous in mathematical modeling. Yet, many such equations are
too singular to admit classical treatment. In this article we review some recent progress in …

We study the Langevin dynamics of a U (1) lattice gauge theory on the two-dimensional
torus, and prove that they converge for short time in a suitable gauge to a system of …

The (elliptic) stochastic quantization equation for the (massive) $\cosh (\beta\varphi) _2 $
model, for the charged parameter in the $ L^ 2$ regime (ie $\beta^ 2< 4\pi $), is studied. We …

In this work, we show a convergence result for the discrete formulation of the generalised
KPZ equation∂ tu=(Δ u)+ g (u)(∇ u) 2+ k (∇ u)+ h (u)+ f (u) ξ t (x), where ξ is real-valued, Δ …