Pluripotential theory and convex bodies: large deviation principle
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
We continue the study in  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.
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