On the zeros of random harmonic polynomials: The truncated model

Motivated by Wilmshurst's conjecture and more recent work of W. Li and A. Wei [17], we determine asymptotics for the number of zeros of random harmonic polynomials sampled from the truncated model, recently proposed by J. Hauenstein, D. Mehta, and the authors [10]. Our results confirm (and sharpen) their (3/2)(3/2)-powerlaw conjecture [10] that had been formulated on the basis of computer experiments; this outcome is in contrast with that of the model studied in [17]. For the truncated model we also observe a phase-transition in the complex plane for the Kac–Rice density.