For certain ensembles of random polynomials we give the expected value of the zero distribution (in one variable) and the expected value of the distribution of common zeros of m polynomials (in m variables).
A subset K of ℂⁿ is said to be regular in the sense of pluripotential theory if the pluricomplex Green function (or Siciak extremal function) is continuous in ℂⁿ. We show that K is regular if the intersections of K with sufficiently many complex lines are regular (as subsets of ℂ). A complete characterization of regularity for Reinhardt sets is also given.