Pluripotential Energy and Large Deviation

We generalize results from [13] relating pluripotential energy to the electrostatic energy of a measure given in [5]. As a consequence, we obtain a large deviation principle for a canonical sequence of probability measures on a non-pluripolar compact set K ⊂ ℂn. This is a special case of a result of...

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Bibliographic Details
Published in:Indiana University mathematics journal 2013-01, Vol.62 (2), p.523-550
Main Authors: Bloom, Thomas, Levenberg, Norman
Format: Article
Language:English
Subjects:
College mathematics
Electrostatics
Energy
Entropy
Mathematical theorems
Polynomials
Potential theory
Topological theorems
Topology
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Summary:We generalize results from [13] relating pluripotential energy to the electrostatic energy of a measure given in [5]. As a consequence, we obtain a large deviation principle for a canonical sequence of probability measures on a non-pluripolar compact set K ⊂ ℂn. This is a special case of a result of R. Berman [3]. For n = 1, we include a proof that uses only standard techniques of weighted potential theory.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2013.62.4930