  We consider the nodal domains of Gaussian random waves in two dimensions. We
present a method to calculate the distribution of the number of nodal domains
and the average connectivity with the help of auxiliary Potts-spins. An
analytical approach could be helpful to decide whether the pattern of nodal
domains belongs to the universality class of short-ranged percolation. This is
not completely evident since we find (weak) long-ranged correlations between
distant avoided nodal intersections.
