  We show that a Wigner induced random orthonormal basis of spherical harmonics
is almost surely quantum ergodic. Here, a random basis is identified with an
element of the product probability space of unitary groups, each endowed with
the measure induced by the generalized Wigner ensemble. This yields a
semi-classical realization of the probabilistic quantum unique ergodicity
result for Wigner eigenvectors of Bourgade-Yau. At the same time, this
generalizes a similar result due to Zelditch, who uses Haar measure on the
unitary groups in defining the notion of a random basis.
