  Typical eigenstates of quantum systems, whose classical limit is chaotic, are
well approximated as random states. Corresponding eigenvalue spectra is modeled
through appropriate ensemble of random matrix theory. However, a small subset
of states violate this principle and display eigenstate localization, a
counter-intuitive feature known to arise due to purely quantum or semiclassical
effects. In the spectrum of chaotic systems, the localized and random states
interact with one another and modifies the spectral statistics. In this work, a
$3 \times 3$ random matrix model is used to obtain exact result for the ratio
of spacing between a generic and localized state. We consider
time-reversal-invariant as well as non-invariant scenarios. These results agree
with the spectra computed from realistic physical systems that display
localized eigenmodes.
