Exact statistical properties of the zeros of complex random polynomials

The zeros of complex Gaussian random polynomials, with coefficients such th at the density in the underlying complex space is uniform, are known to hav e the same statistical properties as the zeros of the coherent state repres entation of one-dimensional chaotic quantum systems. We extend the interpre tation of these polynomials by showing that they also arise as the wavefunc tion for a quantum particle in a magnetic field constructed from a random s uperposition of states in the lowest Landau level. A study of the statistic al properties of the zeros is undertaken using exact formulae for the one- and two-point distribution functions. Attention is focused on the moments o f the two-point correlation in the bulk, the variance of a linear statistic , and the asymptotic form of the two-point correlation at the boundary. A c omparison is made with the same quantities for the eigenvalues of complex G aussian random matrices.