How many roots of a system of random Laurent polynomials are real?

نویسندگان

چکیده

The expected number of zeros a random real polynomial degree $N$ asymptotically equals $\frac{2}{\pi}\log N$. On the other hand, average fraction trigonometric increasing converges to not $0$ but $1/\sqrt 3$. An roots system polynomials in several variables is equal mixed volume some ellipsoids depending on degrees polynomials. Comparing this formula with Theorem BKK we prove that phenomenon nonzero remains valid.

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ژورنال

عنوان ژورنال: Sbornik Mathematics

سال: 2022

ISSN: ['1064-5616', '1468-4802']

DOI: https://doi.org/10.1070/sm9559