Abstract: The Berry random wave conjecture predicts that chaotic eigenfunctions should locally resemble Gaussian random fields. A parallel phenomenon occurs for eigenvectors of large random matrices. I will explain how bulk eigenvectors of Wigner-type matrices can be tested through deterministic observables A, leading to overlap ⟨u,Au⟩ whose fluctuations are asymptotically Gaussian. When the observable varies in a parameter t, these fluctuations converge to Gaussian processes giving a scaling-limit theory for certain eigenvector statistics.