  We define a determinantal point process on the complex projective space that
reduces to the so-called spherical ensemble for complex dimension 1 under
identification of the 2-sphere with the Riemann sphere. Through this
determinantal point process we propose a point processs in odd-dimensional
spheres that produces fairly well-distributed points, in the sense that the
expected value of the Riesz 2-energy for these collections of points is smaller
than all previously known bounds.
