  In this work we study the point spectra of selfadjoint Sturm-Liouville
operators with generalized point interactions, where the two one-sided limits
of the solution data are related via a general $\mathrm{SL}(2,\mathbb{R})$
matrix. We are particularly interested in the stability of eigenvalues with
respect to the variation of the parameters of the interaction matrix. As a
particular application to the case of random generalized point interactions we
establish a version of Pastur's theorem, stating that except for degenerate
cases, any given energy is an eigenvalue only with probability zero. For this
result, independence is important but identical distribution is not required,
and hence our result extends Pastur's theorem from the ergodic setting to the
non-ergodic setting.
