On random surface area

Abstract

Consider a random smooth Gaussian field G(x): $ F \to \mathbb{R} $ , where F is a compact set in $ {\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.