Random Riesz energies on compact Kähler manifolds

The expected Riesz energies E μ h N E s Eμ ^N_h Eₛ of the zero sets of systems of independent Gaussian random polynomials of degree N N are determined asymptotically as the degree N → ∞ N → ∞ in all dimensions and codimensions. The asymptotics are proved for sections of any positive line bundle over any compact Kähler manifold.