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Weyl law for the Anderson Hamiltonian on a two-dimensional manifold (2009.03549v4)
Published 8 Sep 2020 in math.AP, math-ph, math.MP, math.PR, and math.SP
Abstract: We define the Anderson Hamiltonian H on a two-dimensional manifold using high order paracontrolled calculus. It is a self-adjoint operator with pure point spectrum. We get lower and upper bounds on its eigenvalues which imply an almost sure Weyl-type law for H.
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