108 citations · 614 across the 35 of their papers we have counts for
40 papers
Phase transition for invariant measures of the focusing Schrödinger equation
Leonardo Tolomeo, Hendrik Weber
We consider the Gibbs measure for the focusing nonlinear Schrödinger equation on the one-dimensional torus , that was introduced in a seminal paper by Lebowitz, Rose and…
Martingale-driven integrals and singular SPDEs
Paolo Grazieschi, Konstantin Matetski, Hendrik Weber
We consider multiple stochastic integrals with respect to càdlàg martingales, which approximate a cylindrical Wiener process. We define a chaos expansion, analogous to the case of…
The dynamical Ising-Kac model in 3D converges to
Paolo Grazieschi, Konstantin Matetski, Hendrik Weber
We consider the Glauber dynamics of a ferromagnetic Ising-Kac model on a three-dimensional periodic lattice of size , in which the flipping rate of each spin depends on…
Brownian particle in the curl of 2-d stochastic heat equations
Guilherme L. Feltes, Hendrik Weber
We study the long time behaviour of a Brownian particle evolving in a dynamic random environment. Recently, [G. Cannizzaro, L. Haunschmid-Sibitz, F. Toninelli, preprint arXiv:2106.…
Optimal regularity in time and space for stochastic porous medium equations
Stefano Bruno, Benjamin Gess, Hendrik Weber
We prove optimal regularity estimates in Sobolev spaces in time and space for solutions to stochastic porous medium equations. The noise term considered here is multiplicative, whi…
Feature Engineering with Regularity Structures
Ilya Chevyrev, Andris Gerasimovics, Hendrik Weber
We investigate the use of models from the theory of regularity structures as features in machine learning tasks. A model is a polynomial function of a space-time signal designed to…
A priori bounds for quasi-linear SPDEs in the full sub-critical regime
Felix Otto, Jonas Sauer, Scott Smith +1
This paper is concerned with quasi-linear parabolic equations driven by an additive forcing , in the full sub-critical regime . We are inspired by Hairer'…
A priori bounds for rough differential equations with a non-linear damping term
Timothee Bonnefoi, Ajay Chandra, Augustin Moinat +1
We consider a rough differential equation with a non-linear damping drift term: \begin{align*} dY(t) = - |Y|^{m-1} Y(t) dt + σ(Y(t)) dX(t), \end{align*} where is a branched rou…
Phase transitions for
Ajay Chandra, Trishen S. Gunaratnam, Hendrik Weber
We establish a surface order large deviation estimate for the magnetisation of low temperature . As a byproduct, we obtain a decay of spectral gap for its Glauber dynamics g…
A priori bounds for the equation in the full sub-critical regime
Ajay Chandra, Augustin Moinat, Hendrik Weber
We derive a priori bounds for the equation in the full sub-critical regime using Hairer's theory of regularity structures. The equation is formally given by \begin{equation}…
Local bounds for stochastic reaction diffusion equations
Augustin Moinat, Hendrik Weber
We prove a priori bounds for solutions of stochastic reaction diffusion equations with super-linear damping in the reaction term. These bounds provide a control on the supremum of…
Exponential loss of memory for the 2-dimensional Allen-Cahn equation with small noise
Pavlos Tsatsoulis, Hendrik Weber
We prove an asymptotic coupling theorem for the -dimensional Allen--Cahn equation perturbed by a small space-time white noise. We show that with overwhelming probability two pro…
Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions
Trishen S. Gunaratnam, Tadahiro Oh, Nikolay Tzvetkov +1
We prove quasi-invariance of Gaussian measures supported on Sobolev spaces under the dynamics of the three-dimensional defocusing cubic nonlinear wave equation. As in the previous…
Parabolic equations with rough coefficients and singular forcing
Felix Otto, Jonas Sauer, Scott Smith +1
This article focuses on parabolic equations with rough diffusion coefficients which are ill-posed in the classical sense of distributions due to the presence of a singular forcing.…
Quasilinear SPDEs in divergence-form
Felix Otto, Hendrik Weber
We develop a solution theory in Hölder spaces for a quasilinear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE Lemmas which establish a p…
The Schr{ö}dinger equation with spatial white noise potential
Arnaud Debussche, Hendrik Weber
We consider the linear and nonlinear Schr{ö}dinger equation with a spatial white noise as a potential in dimension 2. We prove existence and uniqueness of solutions thanks to a cha…
Gaussian Approximations for Probability Measures on
Yulong Lu, Andrew M. Stuart, Hendrik Weber
This paper concerns the approximation of probability measures on with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the exi…
Construction of diagrams for pedestrians
Jean-Christophe Mourrat, Hendrik Weber, Weijun Xu
We aim to give a pedagogic and essentially self-contained presentation of the construction of various stochastic objects appearing in the dynamical model. The construction…
Spectral Gap for the Stochastic Quantization Equation on the 2-dimensional Torus
Pavlos Tsatsoulis, Hendrik Weber
We study the long time behavior of the stochastic quantization equation. Extending recent results by Mourrat and Weber we first establish a strong non-linear dissipative bound that…
Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits
Hao Shen, Hendrik Weber
We study the Glauber dynamics of a two dimensional Blume-Capel model (or dilute Ising model) with Kac potential parametrized by - the "inverse temperature" and the "chemica…
Quasilinear SPDEs via rough paths
Felix Otto, Hendrik Weber
We are interested in (uniformly) parabolic PDEs with a nonlinear dependance of the leading-order coefficients, driven by a rough right hand side. For simplicity, we consider a spac…
Gaussian approximations for transition paths in Brownian dynamics
Yulong Lu, Andrew M. Stuart, Hendrik Weber
This paper is concerned with transition paths within the framework of the overdamped Langevin dynamics model of chemical reactions. We aim to give an efficient description of typic…
An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two
Nils Berglund, Giacomo Di Gesù, Hendrik Weber
We study spectral Galerkin approximations of an Allen--Cahn equation over the two-dimensional torus perturbed by weak space-time white noise of strength . We in…
Sample path large deviations for Laplacian models in -dimensions
Stefan Adams, Alexander Kister, Hendrik Weber
For Laplacian models in dimension we derive sample path large deviations for the profile height function, that is, we study scaling limits of Gaussian integrated random wal…