@article{1938,
  abstract     = {We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2.},
  author       = {Pausinger, Florian and Steinerberger, Stefan},
  journal      = {Physics Letters, Section A},
  number       = {6},
  pages        = {535 -- 541},
  publisher    = {Elsevier},
  title        = {{On the distribution of local extrema in quantum chaos}},
  doi          = {10.1016/j.physleta.2014.12.010},
  volume       = {379},
  year         = {2015},
}