The continuous Anderson hamiltonian on a two-dimensional manifold

Abstract: We construct the continuous Anderson hamiltonian driven by a white noise on a compact two-dimensional manifold. We use the paracontrolled calculus to define a dense domain that depends on an enhanced noise built through a renormalisation step, in the spirit of the recent works on singular SPDEs. Using the Babuška-Lax-Milgram theorem, it yields a self-adjoint operator with pure point spectrum and we have estimates for the eigenvalues.

Frenchprobability

Audience: researchers in the topic

Les probabilités de demain webinar

Series comments: There will be no seminar on 1st June because it is a public holiday in France (Pentecôte). The session on 15th June is the last one.