Pluripotential theory and convex bodies

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.
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