Bayraktar, Turgay and Bloom, Thomas and Levenberg, Norman and Lu, Chinh H. (2019) Pluripotential theory and convex bodies: large deviation principle. Arkiv for Matematik, 57 (2). pp. 247-283. ISSN 0004-2080 (Print) 1871-2487 (Online)
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Official URL: http://dx.doi.org/10.4310/ARKIV.2019.v57.n2.a2
Abstract
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-Amp\`ere equation in an appropriate finite energy class. This is achieved using a variational approach.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | convex body; P-extremal function; large deviation principle |
| Subjects: | Q Science > QA Mathematics > QA299.6-433 Analysis |
| Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |
| Depositing User: | Turgay Bayraktar |
| Date Deposited: | 03 Dec 2019 15:39 |
| Last Modified: | 27 Jul 2023 23:26 |
| URI: | https://research.sabanciuniv.edu/id/eprint/39473 |
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Pluripotential theory and convex bodies: large deviation principle. (deposited 04 Aug 2019 22:56)
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