On the zeros of random harmonic polynomials: The truncated model
نویسندگان
چکیده
منابع مشابه
On the Zeros of Random Harmonic Polynomials: the Truncated Model
Inspired by Wilmshurst’s conjecture, W. Li and A. Wei (2009) initiated a probabilistic study concerning the zeros of harmonic polynomials. They derived a Kac-Rice type formula for the expected number of zeros of random harmonic polynomials p(z) + q(z) with independent Gaussian coefficients. They also provided asymptotics in the case when p and q are sampled independently from the the (complex) ...
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15 صفحه اولExperiments on the Zeros of Harmonic Polynomials Using Certified Counting
Motivated by Wilmshurst’s conjecture, we investigate the zeros of harmonic polynomials. We utilize a certified counting approach which is a combination of two methods from numerical algebraic geometry: numerical polynomial homotopy continuation to compute a numerical approximation of each zero and Smale’s alpha-theory to certify the results. Using this approach, we provide new examples of harmo...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2016
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2016.02.039