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pro vyhledávání: '"Zachhuber, Immanuel"'
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 exploiting the stochastic optimal control formulation of Gibbs measures. U
Externí odkaz:
http://arxiv.org/abs/2309.01635
Autor:
Zachhuber, Immanuel
We prove finite speed of propagation for the multiplicative stochastic wave equation in two and three dimensions which leads us to a global space-time well-posedness result for the cubic nonlinear equation in the analogue of the energy space.
Externí odkaz:
http://arxiv.org/abs/2110.08086
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:
Zachhuber, Immanuel
We study Strichartz estimates with very rough potentials, the spatial white noise on the 2 dimensional torus being of particular interest. Applications include solving the multiplicative stochastic NLS with general integer powers in a low-regularity
Externí odkaz:
http://arxiv.org/abs/1911.01982
We analyze nonlinear Schr\"odinger and wave equations whose linear part is given by the renormalized Anderson Hamiltonian in two and three dimensional periodic domains.
Externí odkaz:
http://arxiv.org/abs/1807.06825
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