article

Title: Pluripotential energy and large deviation

Authors: Thomas Bloom and Norman Levenberg

Issue: Volume 62 (2013), Issue 2, 523-550

Abstract:

$We generalize results from [Th. Bloom and N. Levenberg, \textit{Pluripotential energy}, Potential Anal. \textbf{36} (2012), no. 1, 155--176] relating pluripotential energy to the electrostatic energy of a measure given in [R. Berman, S. Boucksom, V. Guedj, and A. Z\'eriahi, \textit{A variational approach to complex Monge-Ampere equations}, preprint, available at http://arxiv.org/abs/arXiv:0907.4490]. As a consequence, we obtain a large deviation principle for a canonical sequence of probability measures on a nonpluripolar compact set $K\subset\mathbb{C}^n$. This is a special case of a result of R. Berman [Determinantal point processes and fermions on complex manifolds: large deviations and bosonization, preprint, available at http://arxiv.org/abs/arXiv:0812.4224v2]. For $n=1$, we include a proof that uses only standard techniques of weighted potential theory.$