2D random magnetic Laplacian with white noise magnetic field

Léo Morin (1, 2) , Antoine Mouzard (1, 2)

1 UR - Université de Rennes
2 IRMAR - Institut de Recherche Mathématique de Rennes

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 functions in L 2. We give sharp bounds on the eigenvalues which imply an almost sure Weyl-type law.

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Probabilités [math.PR]

Léo Morin, Antoine Mouzard. 2D random magnetic Laplacian with white noise magnetic field. Stochastic Processes and their Applications, 2022, 142, pp.160-184. ⟨10.1016/j.spa.2021.10.004⟩. ⟨hal-03107403v2⟩