Abstract: We consider quadratic forms evaluated at GOE/GUE eigenvectors, like those studied in the context of quantum unique ergodicity. Under a rank assumption, we show that, in order to compute their extremal statistics, it suffices to replace the eigenvectors with independent Gaussian vectors. By carrying out some representative Gaussian computations, we thus find Gumbel and Weibull limiting distributions for the original problem. Joint work with László Erdős.