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arXiv · 2606.19075

Random Schr\"odinger operators on manifolds and abstract bounds for multiplier-type operators

Jean-Claude Cuenin·Konstantin Merz·Eduard Stefanescu
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Abstract

We study random Schr\"odinger operators on closed Riemannian manifolds with Anderson-type potentials. We prove high-probability spectral inclusion bounds showing that eigenvalues remain close to those of the Laplacian, with deviations controlled by a norm of the potential coefficients. Compared with deterministic bounds, this yields a square-root cancellation gain. The proof is based on a general principle showing that randomisation improves operator norm bounds for multiplier-type operators, which we formulate in both discrete and continuous settings.

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Jean-Claude Cuenin, Konstantin Merz, Eduard Stefanescu. 2026-06-17. Random Schr\"odinger operators on manifolds and abstract bounds for multiplier-type operators. https://arxiv.org/abs/2606.19075

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