Using spectral multiplicities of the Laplacian acting on the standard
two-torus, we endow the each eigenspace with a Gaussian probability
measure. This induces a notion of a random eigenfunctions on the torus,
and we study the statistics of nodal lengths of the eigenfunctions in
the high energy limit. In particular, we determine the variance for a
generic sequence of energy levels, and also find that the variance can
be different for certain "degenerate" subsequences.
