Almost all eigenfunctions of a rational polygon are uniformly   distributed
  We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational polygon. The modulus squared of the eigenfunctions defines a sequence of probability measures. We prove that this sequence contains a density-one subsequence that converges to Lebesgue measure. 
Jens Marklof and Zeev Rudnick
math-ph math.MP math.SP nlin.CD