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 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 …

Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized
version of the three-dimensional stochastic nonlinear wave equation with quadratic …

We solve multidimensional SDEs with distributional drift driven by symmetric, α-stable Lévy
processes for α∈(1, 2] by studying the associated (singular) martingale problem and by …

Abstract We define the Anderson Hamiltonian H on a two-dimensional manifold using the
high order paracontrolled calculus. It is a self-adjoint operator with pure point spectrum. We …

We consider the stochastic differential equation on ℝ d given by d X t= b (t, X t) dt+ d B t,
where B is a Brownian motion and b is considered to be a distribution of regularity>− 1 2. We …

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 …