Expected Density of Complex Zeros of Random Hyperbolic Polynomials

AV Grigorash, K Farahmand

    Research output: Contribution to journalArticlepeer-review

    Original languageEnglish
    Pages (from-to)389-393
    JournalApplied Mathematics Letters
    Volume15
    Issue number3
    DOIs
    Publication statusPublished - 1 May 2002

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    The expected number of real zeros of a hyperbolic polynomial with real random coefficients is known. In this paper for the first time we study the case of complex coefficients. The density of the complex zeros of such a polynomial is obtained. We also highlight how our results can be modified to yield the result for other types of polynomials. We show that the complex zeros of a random hyperbolic polynomial are distributed approximately uniformly along the imaginary axis, as the degree of the polynomial tends to infinity.

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