Pluripotential theory and convex bodies
Sbornik. Mathematics, Tome 209 (2018) no. 3, pp. 352-384
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A seminal paper by Berman and Boucksom exploited ideas from complex geometry to analyze the asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles $L$ over compact, complex manifolds as the power grows. This yielded results on weighted polynomial spaces in weighted pluripotential theory in $\mathbb{C}^d$. Here, motivated by a recent paper by the first author on random sparse polynomials, we work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in $(\mathbb{R}^+)^d$. These classes of polynomials need not occur as sections of tensor powers of a line bundle $L$ over a compact, complex manifold. We follow the approach of Berman and Boucksom to obtain analogous results.
Bibliography: 16 titles.
Keywords:
convex body, $P$-extremal function.
@article{SM_2018_209_3_a3,
author = {T. Bayraktar and T. Bloom and N. Levenberg},
title = {Pluripotential theory and convex bodies},
journal = {Sbornik. Mathematics},
pages = {352--384},
publisher = {mathdoc},
volume = {209},
number = {3},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2018_209_3_a3/}
}
T. Bayraktar; T. Bloom; N. Levenberg. Pluripotential theory and convex bodies. Sbornik. Mathematics, Tome 209 (2018) no. 3, pp. 352-384. http://geodesic.mathdoc.fr/item/SM_2018_209_3_a3/