Motivated by Wilmshurst's conjecture and more recent work of W. Li and A. Wei , 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 . Our results confirm (and sharpen) their (3/2)-powerlaw conjecture  that had been formulated on the basis of computer experiments; this outcome is in contrast with that of the model studied in . For the truncated model we also observe a phase-transition in the complex plane for the Kac-Rice density. © 2016.
|Titolo:||On the zeros of random harmonic polynomials: the truncated model|
|Autori:||Lerario, A.; Lundberg, E.|
|Rivista:||JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS|
|Data di pubblicazione:||2016|
|Digital Object Identifier (DOI):||10.1016/j.jmaa.2016.02.039|
|Appare nelle tipologie:||1.1 Journal article|