On Distribution of Zeros of Random Polynomials in Complex Plane
By I. Ibragimov, Dmitry Zaporozhets. 2011
94 citations recorded by the source corpus.
Let \(G_{n}(z) = \xi _{0} + \xi _{1}z + \cdots + \xi _{n}{z}^{n}\) be a random polynomial with i.i.d. coefficients (real or complex). We show that the arguments of the roots of G n (z) are uniformly distributed in [0, 2π] asymptotically as \(n\,\rightarrow \,\infty \). We also prove that the condition \(\mathbf{E}\,\ln (1 + \vert \xi _{0}\vert )\,<\,\infty \) is necessary and sufficient for the roots to asymptotically concentrate near the unit circumference.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7987a37141c7b2496f547e98e8e6eec80509741c
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Equidistribution of zeros of random holomorphic sections (2013, unknown): “Recently, Ibragimov and Zaporozhets [24] provided a necessary and sufficient condition for global universality of zero distribution for Kac ensembles (see (1.4)).”
- Asymptotic distribution of complex zeros of random analytic functions (2014, background): “Then, Ibragimov and Zaporozhets [16] proved that the following two conditions are equivalent: (1) With probability 1, the sequence of measures 1 nμKn converges as n→ ∞ weakly to the uniform probability distribution on T.”