Pluripotential energy and large deviation

TL;DR

This paper extends the connection between pluripotential energy and electrostatic energy, establishing a large deviation principle for measures on complex sets, with a simplified proof for the one-dimensional case.

Contribution

It generalizes previous results linking pluripotential and electrostatic energies and provides a new proof for the one-dimensional case using standard potential theory techniques.

Findings

Established a large deviation principle for measures on nonpluripolar sets in C^n.

Unified pluripotential and electrostatic energy frameworks.

Simplified proof for the one-dimensional case.

Abstract

We generalize our previous results relating pluripotential energy with the electrostatic energy of a measure given by Berman, Boucksom, Guedj and Zeriahi. As a consequence, we obtain a large deviation principle for a canonical sequence of probability measures on a nonpluripolar compact set K in C^n. This is a special case of a result of R. Berman. For n=1, we include a proof that uses only standard techniques of weighted potential theory.