The spectrum of a large class of one-dimensional continuous random Schrödinger operators is number rigid under growth conditions on the deterministic potential, proved via Feynman-Kac variance estimates for exponential linear statistics.
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Spectral rigidity of random Schr\"odinger operators via Feynman-Kac formulas
The spectrum of a large class of one-dimensional continuous random Schrödinger operators is number rigid under growth conditions on the deterministic potential, proved via Feynman-Kac variance estimates for exponential linear statistics.