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 continuous Anderson operator $ H=\Delta+\xi $ on a two dimensional
closed Riemannian manifold $\mathcal {S} $. We provide a short self-contained functional …

We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and
an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove …

We solve the Schrödinger equation with logarithmic nonlinearity and multiplicative spatial
white noise on\({\mathbb {R}}^ d\) with\(d\le 2\). Because of the nonlinearity, the regularity …

Using an approach introduced by Hairer–Labbé we construct a unique global dynamics for
the NLS on T 2 with a white noise potential and an arbitrary polynomial nonlinearity. We …

In this work, we study the Cauchy problem for a class of dispersive PDEs where a rough time
coefficient is present in front of the dispersion. Under minimal assumptions on the …

We provide a simple construction of the Anderson operator in dimensions two and three.
This is done through its quadratic form. We rely on an exponential transform instead of the …

We study the Gaussian measure whose covariance is related to the Anderson Hamiltonian
operator, proving that it admits a regular coupling to the (standard) Gaussian free field …

We define the random magnetic Laplacian with spatial white noise as magnetic field on the
two-dimensional torus using paracontrolled calculus. It yields a random self-adjoint operator …

We study the parabolic defocusing stochastic quantization equation with both mutliplicative
spatial white noise and an independant space-time white noise forcing, on compact …