The morphology of nodal lines - random waves versus percolation

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.