Pluripotential theory and convex bodies

Official URL: http://dx.doi.org/10.1070/SM8893

A seminal paper of Berman and Boucksom exploited ideas from complex geometry to analyze 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 C^d. Here, motivated from a recent paper of 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 $R^d_+$. 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 recover analogous results.