Geodesic
On the Euler characteristic of a~random algebraic hypersurface
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 224-230

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We calculate the mean value of the Euler characteristic of the hypersurface in $\mathbb R P^d$ ($d$ odd) defined by a random polynomial of given degree under the condition that the polynomial has normal distribution with zero mean invariant with respect to the action of the orthogonal group $O(d+1)$. 
@article{ZNSL_1998_252_a19,
     author = {S. S. Podkorytov},
     title = {On the {Euler} characteristic of a~random algebraic hypersurface},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {224--230},
     publisher = {mathdoc},
     volume = {252},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a19/}
}
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S. S. Podkorytov. On the Euler characteristic of a~random algebraic hypersurface. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 224-230. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a19/