Random Riesz energies on compact Kähler manifolds

Feng, Renjie; Zelditch, Steve

doi:10.1090/S0002-9947-2013-05870-9

Random Riesz energies on compact Kähler manifolds
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by Renjie Feng and Steve Zelditch PDF

Trans. Amer. Math. Soc. 365 (2013), 5579-5604 Request permission

Abstract:

The expected Riesz energies $E_{\mu ^N_h}\mathcal E_{s}$ of the zero sets of systems of independent Gaussian random polynomials of degree $N$ are determined asymptotically as the degree $N \rightarrow \infty$ in all dimensions and codimensions. The asymptotics are proved for sections of any positive line bundle over any compact Kähler manifold.

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