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2D random magnetic Laplacian with white noise magnetic field

Mathematical Physics 2021-07-09 v2 math.MP Probability Spectral Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2101.05020,
  title  = {2D random magnetic Laplacian with white noise magnetic field},
  author = {Léo Morin and Antoine Mouzard},
  journal= {arXiv preprint arXiv:2101.05020},
  year   = {2021}
}