  We investigate the number of nodal intersections of random Gaussian Laplace
eigenfunctions on the standard two-dimensional flat torus ("arithmetic random
waves") with a fixed real-analytic reference curve with nonvanishing curvature.
The expected intersection number is universally proportional to the length of
the reference curve, times the wavenumber, independent of the geometry.
  Our main result prescribes the asymptotic behaviour of the nodal
intersections variance for analytic curves in the high energy limit;
remarkably, it is dependent on both the angular distribution of lattice points
lying on the circle with radius corresponding to the given wavenumber, and the
geometry of the given curve. In particular, this implies that the nodal
intersection number admits a universal asymptotic law with arbitrarily high
probability.
