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arXiv · 1807.11369

Pluripotential Theory and Convex Bodies: Large Deviation Principle

Turgay Bayraktar·Thomas Bloom·Norman Levenberg·Chinh H. Lu
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Abstract

We continue the study in a previous work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body $P$ in $({\bf R}^+)^d$. Our goal is to establish a large deviation principle in this setting specifying the rate function in terms of $P-$pluripotential-theoretic notions. As an important preliminary step, we first give an existence proof for the solution of a Monge-Amp\`ere equation in an appropriate finite energy class. This is achieved using a variational approach.

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Turgay Bayraktar, Thomas Bloom, Norman Levenberg, Chinh H. Lu. 2018-07-30. Pluripotential Theory and Convex Bodies: Large Deviation Principle. https://arxiv.org/abs/1807.11369

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