Zobrazeno 1 - 10
of 252
pro vyhledávání: '"Mouzard A"'
Autor:
Debussche, Arnaud, Mouzard, Antoine
In this paper, we continue some investigations on the periodic NLSE started by Lebowitz, Rose and Speer and by Bourgain with the addition of a distributional multiplicative potential. We prove that the equation is globally wellposed for a set of data
Externí odkaz:
http://arxiv.org/abs/2405.00583
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity. After renormalizing the nonlinearity
Externí odkaz:
http://arxiv.org/abs/2401.12742
Autor:
Mouzard, Antoine, Ouhabaz, El Maati
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 regularity structures or paracontrolled calculus which are usually used
Externí odkaz:
http://arxiv.org/abs/2309.02821
Autor:
Chauleur, Quentin, Mouzard, Antoine
We solve the Schr{\"o}dinger equation with logarithmic nonlinearity and multiplicative spatial white noise on R d with d $\le$ 2. Because of the nonlinearity, the regularity structures and the paracontrolled calculus can not be used. To solve the equ
Externí odkaz:
http://arxiv.org/abs/2308.15814
Autor:
Faou, Erwan, Mouzard, Antoine
We start from the remark that in wave turbulence theory, exemplified by the cubic twodimensional Schr{\"o}dinger equation (NLS) on the real plane, the regularity of the resonant manifold is linked with dispersive properties of the equation and thus w
Externí odkaz:
http://arxiv.org/abs/2307.01774
Autor:
Mouzard, Antoine
We construct the infinitesimal generator of the Brox diffusion on a line with a periodic Brownian environment. This gives a new construction of the process and allows to solve the singular martingale problem. We prove that the associated semigroup is
Externí odkaz:
http://arxiv.org/abs/2212.10840
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 analysis construction of the operator as an unbounded operator on $L^2(\mathcal{S}
Externí odkaz:
http://arxiv.org/abs/2201.04705
Autor:
Mouzard, Antoine, Zachhuber, Immanuel
Publikováno v:
Analysis & PDE 17 (2024) 421-454
We prove Strichatz inequalities for the Schr{\"o}dinger equation and the wave equation with multiplicative noise on a two-dimensional manifold. This relies on the Anderson Hamiltonian H described using high order paracontrolled calculus. As an applic
Externí odkaz:
http://arxiv.org/abs/2104.07940
Autor:
Morin, Léo, Mouzard, Antoine
We define the random magnetic Laplacien with spatial white noise as magnetic field on the two-dimensional torus using paracontrolled calculus. It yields a random self-adjoint operator with pure point spectrum and domain a random subspace of nonsmooth
Externí odkaz:
http://arxiv.org/abs/2101.05020
Autor:
Mouzard, Antoine
We define the Anderson Hamiltonian H on a two-dimensional manifold using high order paracontrolled calculus. It is a self-adjoint operator with pure point spectrum. We get lower and upper bounds on its eigenvalues which imply an almost sure Weyl-type
Externí odkaz:
http://arxiv.org/abs/2009.03549