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2D random magnetic Laplacian with white noise magnetic field

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.
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https://hal.archives-ouvertes.fr/hal-03107403
Contributor : Antoine Mouzard <>
Submitted on : Tuesday, January 12, 2021 - 3:28:50 PM
Last modification on : Friday, January 15, 2021 - 3:08:17 AM

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Magnetic laplacien.pdf
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  • HAL Id : hal-03107403, version 1
  • ARXIV : 2101.05020

Citation

Léo Morin, Antoine Mouzard. 2D random magnetic Laplacian with white noise magnetic field. 2021. ⟨hal-03107403⟩

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