58 citations · 102 across the 8 of their papers we have counts for
11 papers
Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions
Khalil Chouk, Willem van Zuijlen
In this paper we consider the Anderson Hamiltonian with white noise potential on the box with Dirichlet boundary conditions. We show that all the eigenvalues divided by $…
Path-by-path regularization by noise for scalar conservation laws
Khalil Chouk, Benjamin Gess
We prove a path-by-path regularization by noise result for scalar conservation laws. In particular, this proves regularizing properties for scalar conservation laws driven by fract…
An invariance principle for the two-dimensional parabolic Anderson model with small potential
Khalil Chouk, Jan Gairing, Nicolas Perkowski
We prove an invariance principle for the two-dimensional lattice parabolic Anderson model with small potential. As applications we deduce a Donsker type convergence result for a di…
The continuous Anderson hamiltonian in dimension two
Romain Allez, Khalil Chouk
We define the Anderson hamiltonian on the two dimensional torus . This operator is formally defined as where is the Laplacian oper…
Multidimensional SDEs with singular drift and universal construction of the polymer measure with white noise potential
Giuseppe Cannizzaro, Khalil Chouk
We study existence and uniqueness of solution for stochastic differential equations with distributional drift by giving a meaning to the Stroock-Varadhan martingale problem associa…
Support theorem for a singular semilinear stochastic partial differential equation
K. Chouk, P. K. Friz
We consider the generalized parabolic Anderson equation (gPAM) in 2 dimensions with periodic boundary. This is an example of a singular semilinear stochastic partial differential e…
Rough sheets
K. Chouk, M. Gubinelli
Rough sheets are two-parameter analogs of rough paths. In this work the theory of integration over functions of two parameters is extended to cover the case of irregular functions…
Nonlinear PDEs with modulated dispersion II: Korteweg-de Vries equation
Khalil Chouk, Massimiliano Gubinelli, Guopeng Li +2
(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 dispersive equatio…
Paracontrolled Distributions and the 3-dimensional Stochastic Quantization Equation
Rémi Catellier, Khalil Chouk
We prove the existence and uniqueness of a local solution to the periodic renormalized model of stochastic quantisation using the method of controlled distributions introdu…
Skorohod and Stratonovich integration in the plane
Khalil Chouk, Samy Tindel
This article gives an account on various aspects of stochastic calculus in the plane. Specifically, our aim is 3-fold: (i) Derive a pathwise change of variable formula for a path i…
Nonlinear PDEs with modulated dispersion I: Nonlinear Schrödinger equations
K. Chouk, M. Gubinelli
We start a study of various nonlinear PDEs under the effect of a modulation in time of the dispersive term. In particular in this paper we consider the modulated non-linear Schrödi…