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arXiv · 2204.06081

On the expected number of real roots of polynomials and exponential sums

Gregorio Malajovich
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Abstract

The expected number of real projective roots of orthogonally invariant random homogeneous real polynomial systems is known to be equal to the square root of the B\'ezout number. A similar result is known for random multi-homogeneous systems, invariant through a product of orthogonal groups. In this note, those results are generalized to certain families of sparse polynomial systems, with no orthogonal invariance assumed.

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Gregorio Malajovich. 2022-04-12. On the expected number of real roots of polynomials and exponential sums. https://doi.org/10.1016/j.jco.2022.101720

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