Expected Density of Complex Zeros of Random Hyperbolic Polynomials

AV Grigorash; K Farahmand

doi:10.1016/S0893-9659(01)00148-3

Expected Density of Complex Zeros of Random Hyperbolic Polynomials

AV Grigorash, K Farahmand

Research output: Contribution to journal › Article › peer-review

Original language	English
Pages (from-to)	389-393
Journal	Applied Mathematics Letters
Volume	15
Issue number	3
DOIs	https://doi.org/10.1016/S0893-9659(01)00148-3
Publication status	Published - 1 May 2002

Bibliographical note

Other Details
------------------------------------
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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10.1016/S0893-9659(01)00148-3

Cite this

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title = "Expected Density of Complex Zeros of Random Hyperbolic Polynomials",

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note = "Other Details ------------------------------------ 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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