Normalized zero currents of random P-polynomials converge weakly to dd^c of the Legendre-Fenchel transform of the exponential profile over the convex body P.
Bayraktar, Equidistribution of zeros of random holomorphic sections, Indiana Univ.\ Math.\ J.\ 65 (2016), no
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Zeros of random $P$-polynomials in $\mathbb{C}^d$ with exponential profiles
Normalized zero currents of random P-polynomials converge weakly to dd^c of the Legendre-Fenchel transform of the exponential profile over the convex body P.