Large gaps asymptotics for the 1-dimensional random Schr¨odinger operator

Stephanie S.M. Jacquot (University of Cambridge)

Abstract


We show that in the Schr\"{o}dinger 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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Pages: 1-12

Publication Date: November 26, 2014

DOI: 10.1214/ECP.v19-2724

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