  This paper studies the localization behaviour of Bose-Einstein condensates in
disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a
bounded interval. In the regime of weak particle interaction, we are able to
quantify exponential localization of the ground state, depending on statistical
parameters and the strength of the potential. Numerical studies further show
delocalization if we leave the identified parameter range, which is in
agreement with experimental data. These mathematical and numerical findings
allow the prediction of physically relevant regimes where localization of
ground states may be observed experimentally.
