Geodesic
On random surface area
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 154-175 Cet article a éte moissonné depuis la source Math-Net.Ru

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Consider a random smooth Gaussian field $G(x)\colon F\to\mathbb R$, where $F$ is a compact in $\mathbb R^d$. We derive a formula for average area of a surface set by the equation $G(x)=0$ and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of any non-random smooth field. Bibl. 13 titles. 
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D. N. Zaporozhets; I. A. Ibragimov. On random surface area. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 154-175. http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a6/

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