  In this paper we investigate the properties of nodal structures in random
wave fields, and in particular we scrutinize their recently proposed connection
with short-range percolation models. We propose a measure which shows the
difference between monochromatic random waves, which are characterized by
long-range correlations, and Gaussian fields with short-range correlations,
which are naturally assumed to be better modelled by percolation theory. We
also study the relevance of the quantities which we compute to the probability
that nodal lines are in the vicinity of a given reference line.
