In many geostatistical applications (soil contamination evaluation, mining resources estimation), the physical phenomenon under study cannot be observed more than a small number of times. When it is modeled as a random field, this raises the question of how to assess its characteristics from a single realization. To determine when it is even possible, a geostatistical tool named the integral range is introduced. It characterizes the statistical fluctuations of a random field at large scale, and is thus intricately linked to the concepts of ergodicity and mixing. When applied to excursion sets of a max-stable process, we show how it relates to its dependence structure, thereby completing results established by Erwan Koch in a spatial risk context. From this primary analysis, we derive a new estimator of the extremal coefficient function, the spatial asymptotics of which are explored in a continuous domain framework. (Collaboration with Marine Demangeot and Anne Sabourin)