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We study the eigenvector mass distribution of an $N\times N$ Wigner matrix ona set of coordinates $I$ satisfying $| I | \ge c N$ for some constant $c >0$.For eigenvectors corresponding to eigenvalues at the spectral edge, we showthat the sum of the mass on these coordinates converges to a Gaussian in the $N\rightarrow \infty$ limit, after a suitable rescaling and centering. The proofproceeds by a two moment matching argument. We directly compare edgeeigenvector observables of an arbitrary Wigner matrix to those of a Gaussianmatrix, which may be computed explicitly.

Fluctuations in Quantum Unique Ergodicity at the Spectral Edge