Fluctuation of density of states for 1d Schrödinger operators

Abstract

We consider the 1d Schrödinger operator with random decaying potential and compute the 2nd term asymptotics of the density of states, which shows substantial differences between the cases $\alpha >\frac{1}{2}$, $\alpha <\frac{1}{2}$ and $\alpha =\frac{1}{2}$.

References in corpus (1)

• Level statistics for one-dimensional Schrödinger operators and Gaussian beta ensemble

Cited by in corpus (2)

• Limiting distribution of extremal eigenvalues of d-dimensional random Schrödinger operator
• Deviation of top eigenvalue for some tridiagonal matrices under various moment assumptions