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October 2019 Pluripotential theory and convex bodies: large deviation principle
Turgay Bayraktar, Thomas Bloom, Norman Levenberg, Chinh H. Lu
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Ark. Mat. 57(2): 247-283 (October 2019). DOI: 10.4310/ARKIV.2019.v57.n2.a2


We continue the study in [2] in the setting of weighted pluripotential theory arising from polynomials associated to a convex body $P$ in $(\mathbb{R}^{+})^d$. 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–Ampère equation in an appropriate finite energy class. This is achieved using a variational approach.

Funding Statement

N. Levenberg is supported by Simons Foundation grant No. 354549.


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Turgay Bayraktar. Thomas Bloom. Norman Levenberg. Chinh H. Lu. "Pluripotential theory and convex bodies: large deviation principle." Ark. Mat. 57 (2) 247 - 283, October 2019.


Received: 18 August 2018; Revised: 10 February 2019; Published: October 2019
First available in Project Euclid: 16 April 2020

zbMATH: 07114506
MathSciNet: MR4018754
Digital Object Identifier: 10.4310/ARKIV.2019.v57.n2.a2

Primary: 31C15, 32U15, 32U20

Rights: Copyright © 2019 Institut Mittag-Leffler


Vol.57 • No. 2 • October 2019
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