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We analyze the distribution of eigenvectors for mesoscopic, mean-fieldperturbations of diagonal matrices in the bulk of the spectrum. Our resultsapply to a generalized $N\times N$ Rosenzweig-Porter model. We prove that theeigenvectors entries are asymptotically Gaussian with a specific variance,localizing them onto a small, explicit part of the spectrum. For a well spreadinitial spectrum, this variance profile universally follows a heavy-tailedCauchy distribution. In the case of smooth entries, we also obtain a strongform of quantum unique ergodicity as an overwhelming probability bound on theeigenvectors probability mass. The proof relies on a priori local laws for thismodel and the eigenvector moment flow.

Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices