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2014 Large gaps asymptotics for the 1-dimensional random Schrödinger operator
Stephanie Jacquot
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Electron. Commun. Probab. 19: 1-12 (2014). DOI: 10.1214/ECP.v19-2724

Abstract

We show that in the Schrödinger point process, Sch$_\tau$, $\tau>0,$ the probability of having no eigenvalue in a fixed interval of size $\lambda$ is given by \[ \exp\left(-\frac{\lambda^2}{4\tau}+\left(\frac{2}{\tau}-\frac{1}{4}\right)\lambda +o(\lambda)\right), \]as $\lambda\to\infty.$ It is a slightly more precise version than the one given in a previous work.

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Stephanie Jacquot. "Large gaps asymptotics for the 1-dimensional random Schrödinger operator." Electron. Commun. Probab. 19 1 - 12, 2014. https://doi.org/10.1214/ECP.v19-2724

Information

Accepted: 26 November 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1334.60084
MathSciNet: MR3291619
Digital Object Identifier: 10.1214/ECP.v19-2724

Subjects:
Primary: 60G07

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