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

2022/04/12 by Gregorio Malajovich, Malajovich, Gregorio
Mathematics · #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2204.06081

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 Bézout 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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