Weighted polynomials and weighted pluripotential theory

Let $E$ be a compact subset of $\mathbb{C} ^{N}$ and $w\ge 0$ an admissible weight function on $E$. To $(E, w)$ we associate a canonical circular set $Z\subset \mathbb{C} ^{N+1}$. We obtain precise relations between the weighted pluricomplex Green function and weighted equilibrium measure of $(E, w)$ and the pluricomplex Green function and equilibrium measure of $Z$. These results, combined with an appropriate form of the Bernstein-Markov inequality, are used to obtain asymptotic formulas for the leading coefficients of orthonormal polynomials with respect to certain exponentially decreasing weights in $\mathbb{R}^{N}$.