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math.SP2026
Random Schrödinger operators on manifolds and abstract bounds for multiplier-type operators
Jean-Claude Cuenin, Konstantin Merz, Eduard Stefanescu
We study random Schrödinger operators on closed Riemannian manifolds with Anderson-type potentials. We prove high-probability spectral inclusion bounds showing that eigenvalues rem…
math.SP2023
Lieb-Thirring-type inequalities for random Schrödinger operators with complex potentials
Jean-Claude Cuenin, Konstantin Merz
We review some results and proofs on eigenvalue bounds for random Schrödinger operators with complex-valued potentials. We also include new Schatten norm estimates for the resolven…
math.SP2022
Random Schrödinger operators with complex decaying potentials
Jean-Claude Cuenin, Konstantin Merz
We prove that the eigenvalues of a continuum random Schrödinger operator of Anderson type, with complex decaying potential, can be bounded (with high probability) in term…