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Average Euler Characteristic of Random Real Algebraic Varieties
Citation key B-Average-Euler-Characteristic-Of-Random-Real-Algebraic-Varieties
Author Peter Bürgisser
Pages 507-512
Year 2007
Journal Comptes Rendus - Mathematique
Volume 345
Number 9
Abstract We determine the expected curvature polynomial of real projective varieties given as the zero set of independent random polynomials with Gaussian distribution, which is invariant under 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 real solution set of random polynomial equations.
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