Construction of Diagrams for Pedestrians
JC Mourrat, H Weber, W Xu - Meeting on Particle Systems and PDE's, 2015 - Springer
We aim to give a pedagogic and essentially self-contained presentation of the construction
of various stochastic objects appearing in the dynamical\varPhi^ 4_3 model. The …
of various stochastic objects appearing in the dynamical\varPhi^ 4_3 model. The …
On the parabolic and hyperbolic Liouville equations
We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic
damped nonlinear wave equation (SdNLW) with an exponential nonlinearity λ β e^ β u λ β e …
damped nonlinear wave equation (SdNLW) with an exponential nonlinearity λ β e^ β u λ β e …
On the two-dimensional hyperbolic stochastic sine-Gordon equation
We study the two-dimensional stochastic sine-Gordon equation (SSG) in the hyperbolic
setting. In particular, by introducing a suitable time-dependent renormalization for the …
setting. In particular, by introducing a suitable time-dependent renormalization for the …
Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus
We study an optimal mass threshold for normalizability of the Gibbs measures associated
with the focusing mass-critical nonlinear Schrödinger equation on the one-dimensional …
with the focusing mass-critical nonlinear Schrödinger equation on the one-dimensional …
Global well-posedness for the two-dimensional stochastic complex Ginzburg-Landau equation
WJ Trenberth - arXiv preprint arXiv:1911.09246, 2019 - arxiv.org
We study the stochastic complex Ginzburg-Landau equation (SCGL) with an additive space-
time white noise forcing on the two-dimensional torus. This equation is singular and thus we …
time white noise forcing on the two-dimensional torus. This equation is singular and thus we …
A second-quantized kolmogorov–chentsov theorem via the operator product expansion
A Abdesselam - Communications in Mathematical Physics, 2020 - Springer
We establish a direct connection between two fundamental topics: one in probability theory
and one in quantum field theory. The first topic is the problem of pointwise multiplication of …
and one in quantum field theory. The first topic is the problem of pointwise multiplication of …
Strong Convergence of a Splitting Method for the Stochastic Complex Ginzburg-Landau Equation
M Jans, GJ Lord, M Ptashnyk - arXiv preprint arXiv:2412.07206, 2024 - arxiv.org
We consider the numerical approximation of the stochastic complex Ginzburg-Landau
equation with additive noise on the one dimensional torus. The complex nature of the …
equation with additive noise on the one dimensional torus. The complex nature of the …
A nonlinear Schrödinger equation with fractional noise
A Deya, N Schaeffer, L Thomann - Transactions of the American …, 2021 - ams.org
We study a stochastic Schrödinger equation with a quadratic nonlinearity and a space-time
fractional perturbation, in space dimension $ d\leq 3$. When the Hurst index is large …
fractional perturbation, in space dimension $ d\leq 3$. When the Hurst index is large …
Study of a fractional stochastic heat equation
N Schaeffer - arXiv preprint arXiv:2109.11780, 2021 - arxiv.org
In this article, we study a $ d $-dimensional stochastic nonlinear heat equation (SNLH) with
a quadratic nonlinearity, forced by a fractional space-time white noise:\begin …
a quadratic nonlinearity, forced by a fractional space-time white noise:\begin …
On ill-posedness of nonlinear stochastic wave equations driven by rough noise
A Deya - Stochastic Processes and their Applications, 2022 - Elsevier
We highlight a fundamental ill-posedness issue for nonlinear stochastic wave equations
driven by a fractional noise. Namely, if the noise becomes too rough (ie, the sum of its Hurst …
driven by a fractional noise. Namely, if the noise becomes too rough (ie, the sum of its Hurst …