Determinantal structure of the overlaps for induced spherical unitary ensemble

In this paper, we study the determinantal structure of the [Formula: see text]th conditional expectation of the overlap for induced spherical unitary ensemble. We will show the universality for the scaling limits of the [Formula: see text]th conditional expectation of the overlap in the three regimes, strongly non-unitary, weakly non-unitary, and the singular origin regimes.