On the zeros of random harmonic polynomials: the truncated model
Complex Variables
2016-05-16 v2 Probability
Abstract
A probabilistic approach to the study of the number of zeros of complex harmonic polynomials was initiated by W. Li and A. Wei (2009), who derived a Kac-Rice type formula for the expected number of zeros of random harmonic polynomials with independent Gaussian coefficients. They also provided asymptotics for a complex version of the Kostlan ensemble. Here we determine asymptotics for the alternative truncated model that was recently proposed by J. Hauenstein, D. Mehta, and the authors. Our results confirm (and sharpen) their (3/2)-powerlaw conjecture that had been formulated on the basis of computer experiments.
Cite
@article{arxiv.1507.01041,
title = {On the zeros of random harmonic polynomials: the truncated model},
author = {Antonio Lerario and Erik Lundberg},
journal= {arXiv preprint arXiv:1507.01041},
year = {2016}
}
Comments
15 pages, 1 figure. Minor changes in this version include a more detailed proof of Theorem 3