Abstract
We consider quite general h-pseudodifferential operators on R n with small random perturbations and show that in the limit h → 0 the eigenvalues are distributed according to a Weyl law with a probabality that tends to 1. The first author has previously obtained a similar result in dimension 1. Our class of perturbations is different.
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Hager, M., Sjöstrand, J. Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators. Math. Ann. 342, 177–243 (2008). https://doi.org/10.1007/s00208-008-0230-7
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DOI: https://doi.org/10.1007/s00208-008-0230-7