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 ℝm 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.
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Macdonald, B. Density of Complex Zeros of a System of Real Random Polynomials. J Stat Phys 136, 807–833 (2009). https://doi.org/10.1007/s10955-009-9810-5
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DOI: https://doi.org/10.1007/s10955-009-9810-5