The Anderson Hamiltonian on a two-dimensional manifold
Résumé
We define the Anderson Hamiltonian H on a two-dimensional manifold using high order para-controlled calculus. It is a self-adjoint operator with pure point spectrum. We prove estimates on its eigenvalues which imply a Weyl law for H. Finally, we give a version of Brezis-Gallouët inequality which implies existence and uniqueness for the cubic nonlinear Schrödinger equation with multiplicative noise.
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