Pluripotential energy and large deviation

Mathematics – Complex Variables

Scientific paper

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Scientific paper

We generalize our previous results relating pluripotential energy with the energy of a measure given by Berman, Boucksom, Guedj and Zeriahi. We also state and prove a large deviation principle (LDP) for a canonical sequence of probability measures on a compact set K in C^n. For n=1, these include the joint probability distributions of the eigenvalues of unitary ensembles. We give a proof in this case that uses only standard notions and techniques of weighted potential theory.

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