For the spherical and truncated unitary ensembles, diagonal eigenvector overlaps decompose into products of independent variables and converge, conditional on one eigenvalue, to the inverse of a gamma-2 distribution.
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On eigenvector statistics in the spherical and truncated unitary ensembles
For the spherical and truncated unitary ensembles, diagonal eigenvector overlaps decompose into products of independent variables and converge, conditional on one eigenvalue, to the inverse of a gamma-2 distribution.