Average volume, curvatures, and Euler characteristic of random real algebraic varieties

Details Average volume, curvatures, and Euler characteristic of random real algebraic varieties Average volume, curvatures, and Euler characteristic of random real algebraic varieties

2006-06-29

arxiv.org/abs/math/0606755v2

Mathematics

Probability

38 pages. Version 2: corrected typos, changed some notation, rewrote proof of Theorem 5.2

Scientific paper

We determine the expected curvature polynomial of random real projective varieties given as the zero set of independent random polynomials with Gaussian distribution, whose distribution is invariant under the action of the orthogonal group. In particular, the expected Euler characteristic of such random real projective varieties is found. This considerably extends previously known results on the number of roots, the volume, and the Euler characteristic of the solution set of random polynomial equations

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