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Average Euler Characteristic of Random Real Algebraic Varieties
Zitatschlüssel B-Average-Euler-Characteristic-Of-Random-Real-Algebraic-Varieties
Autor Peter Bürgisser
Seiten 507-512
Jahr 2007
Journal Comptes Rendus - Mathematique
Jahrgang 345
Nummer 9
Zusammenfassung 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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