A general expression for the distribution of the maximum of a Gaussian field and the approximation of the tail (Q939394)

The authors study the probability distribution \(F(u)\) of the maximum of smooth Gaussian fields defined on compact subsets of \(\mathbb{R}^d\) having some geometric regularity. The main result is a general implicit expression for the density of \(F\). Explicit bounds for the density as well as improved expansions for \(1-F(u)\) for large \(u\) are deduced.