On random surface area

Details On random surface area On random surface area

2011-02-17

arxiv.org/abs/1102.3509v1

I.~Ibragimov, D.~Zaporozhets. On random surface area (in Russian). {\em Zap. Nauchn. Sem. POMI}, \textbf{384}, 154--175 (2010)

Mathematics

Probability

Scientific paper

Consider a random smooth Gaussian field $G(x):F\to\mathbb{R}$, where $F$ is a
compact in $\mathbb{R}^d$. We derive a formula for average area of a surface
generated 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 a \emph{non-random} smooth field.

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