When a random field (Xt, t € R²) is thresholded on a given level u, the excursion set is given by its indicator 1[u,∞)(Xt). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as e.g. the capacity functional as well as the second moment measure of the boundary length. It extend results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossing theory, in particular Rice methods, and from integral and stochastic geometry.
KRATZ, M. and NAGEL, W. (2014). On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R². ESSEC Business School.