--- res: bibo_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.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Florian foaf_name: Pausinger, Florian foaf_surname: Pausinger foaf_workInfoHomepage: http://www.librecat.org/personId=2A77D7A2-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-8379-3768 - foaf_Person: foaf_givenName: Stefan foaf_name: Steinerberger, Stefan foaf_surname: Steinerberger bibo_doi: 10.1016/j.physleta.2014.12.010 bibo_issue: '6' bibo_volume: 379 dct_date: 2015^xs_gYear dct_language: eng dct_publisher: Elsevier@ dct_title: On the distribution of local extrema in quantum chaos@ ...