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The expected number of real projective roots of orthogonally invariant randomhomogeneous real polynomial systems is known to be equal to the square root ofthe B\'ezout number. A similar result is known for random multi-homogeneoussystems, invariant through a product of orthogonal groups. In this note, thoseresults are generalized to certain families of sparse polynomial systems, withno orthogonal invariance assumed.

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