The asymptotic distribution of Riesz' Energy

Abstract

We consider the asymptotic distribution of the Riesz' energy of a sample of independent and uniformly distributed points on the surface of an hypersphere, when the cardinality of the sample diverges. We identify three asymptotic regimes. In the first regime, both the mean and the variance of the energy exist. In the second regime, only the mean exists. In the third regime, no integer moment exists. We characterize the asymptotic distribution in the three regimes.

Raffaello Seri

Professor of Econometrics

My research interests include statistics, numerical analysis, operations research, psychology, economics and management.