Pluripotential theory and convex bodies: large deviation principle

Turgay Bayraktar Sabanci University Thomas Bloom University of Toronto Norman Levenberg Indiana University Chinh H. Lu Université Paris-Sud

Complex Variables and Complex Analysis mathscidoc:1912.43038

Arkiv for Matematik, 57, (2), 247-283, 2019
We continue the study in [2] in the setting of weighted pluripotential theory arising from polynomials associated to a convex body P in (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.
convex body, P-extremal function, large deviation principle
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@inproceedings{turgay2019pluripotential,
  title={Pluripotential theory and convex bodies: large deviation principle},
  author={Turgay Bayraktar, Thomas Bloom, Norman Levenberg, and Chinh H. Lu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204135039354696594},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={2},
  pages={247-283},
  year={2019},
}
Turgay Bayraktar, Thomas Bloom, Norman Levenberg, and Chinh H. Lu. Pluripotential theory and convex bodies: large deviation principle. 2019. Vol. 57. In Arkiv for Matematik. pp.247-283. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204135039354696594.
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