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Density of Complex Zeros of a System of Real Random Polynomials.

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Title: Density of Complex Zeros of a System of Real Random Polynomials.
Authors: Macdonald, Brian1,2 bmac@jhu.edu
Source: Journal of Statistical Physics. Sep2009, Vol. 136 Issue 5, p807-833. 27p. 4 Graphs.
Subjects: Random polynomials, Density functionals, Mathematical variables, Zero (The number), Linear statistical models
Abstract: We study the density of complex zeros of a system of real random SO( m+1) polynomials in m variables. We show that the density of complex zeros of this random polynomial system with real coefficients rapidly approaches the density of complex zeros in the complex coefficients case. We also show that the behavior the scaled density of complex zeros near ℝ m of the system of real random polynomials is different in the m≥2 case than in the m=1 case: the density approaches infinity instead of tending linearly to zero. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: We study the density of complex zeros of a system of real random SO( m+1) polynomials in m variables. We show that the density of complex zeros of this random polynomial system with real coefficients rapidly approaches the density of complex zeros in the complex coefficients case. We also show that the behavior the scaled density of complex zeros near ℝ m of the system of real random polynomials is different in the m≥2 case than in the m=1 case: the density approaches infinity instead of tending linearly to zero. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10955-009-9810-5
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      – SubjectFull: Mathematical variables
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