2 00 6 Average volume , curvatures , and Euler characteristic of random real algebraic varieties
نویسنده
چکیده
We determine the expected curvature polynomial of random real projec-tive 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 real solution set of random polynomial equations.
منابع مشابه
2 9 Ju n 20 06 Average volume , curvatures , and Euler characteristic of random real algebraic varieties
We determine the expected curvature polynomial of random real projec-tive 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 t...
متن کاملar X iv : m at h / 06 06 65 4 v 2 [ m at h . A T ] 1 6 O ct 2 00 6 EULER CHARACTERISTICS OF ALGEBRAIC VARIETIES
The aim of this note is to study the behavior of intersection homology Euler characteristic under morphisms of algebraic varieties. The main result is a direct application of the BBDG decomposition theorem. Similar formulae for Hodge-theoretic invariants of algebraic varieties were announced by the first and third authors in [4, 11].
متن کاملLipschitz-Killing curvatures of the Excursion Sets of Skew Student's t Random fields
In many real applications related with Geostatistics, medical imaging and material science, the real observations have asymmetric, and heavy-tailed multivariate distributions. These observations are spatially correlated and they could be modelled by the skew random fields. However, certain statistical analysis problems require giving analytical expectations of some integral geometric characteri...
متن کاملThe Euler characteristic of an even-dimensional graph
We write the Euler characteristic χ(G) of a four dimensional finite simple geometric graph G = (V,E) in terms of the Euler characteristic χ(G(ω)) of two-dimensional geometric subgraphs G(ω). The Euler curvature K(x) of a four dimensional graph satisfying the Gauss-Bonnet relation ∑ x∈V K(x) = χ(G) can so be rewritten as an average 1 − E[K(x, f)]/2 over a collection two dimensional “sectional gr...
متن کاملar X iv : m at h / 06 06 65 4 v 3 [ m at h . A T ] 1 J ul 2 00 7 EULER CHARACTERISTICS OF ALGEBRAIC VARIETIES
This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae comparing these two kinds of Euler characteristics. The main results are direct consequences of the calculus of constructible functions and Grothendieck group...
متن کامل