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.
Cite this article
Jens Marklof, Zeév Rudnick, Almost all eigenfunctions of a rational polygon are uniformly distributed. J. Spectr. Theory 2 (2012), no. 1, pp. 107–113