On random surface area |
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Authors: | D. N. Zaporozhets I. A. Ibragimov |
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Affiliation: | (1) DTU Mathematics, Technical University Denmark, Lyngby, Denmark |
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Abstract: | Consider a random smooth Gaussian field G(x): F ? mathbbR F to mathbb{R} , where F is a compact set in mathbbRd {mathbb{R}^d} . We derive a formula for the average area of a surface determined by the equation G(x) = 0 and give some applications. As an auxiliary result, we obtain an integral expression for the area of a surface determined by zeros of a nonrandom smooth field. Bibliography: 13 titles. |
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