2014/10/12 by Igor Rivin, Rivin, Igor
Computer Science · Mathematics · Physics and Astronomy · #05C80 #60B20 #60D05 #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Probability (math.PR) #Spectral Theory (math.SP) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #cs.CG #hep-th #math-ph #math.MP #math.PR #math.SP #msc:05C80 #msc:60B20 #msc:60D05
paper · pdf · doi:10.48550/arxiv.1410.6771
24 pages
arxiv created 2014/10/27 · arxiv updated 2014/10/28
We describe extensive computational experiments on spectral properties of random objects - random cubic graphs, random planar triangulations, and Voronoi and Delaunay diagrams of random (uniformly distributed) point sets on the sphere). We look at bulk eigenvalue distribution, eigenvalue spacings, and locality properties of eigenvectors. We also look at the statistics of nodal domains of eigenvectors on these graphs. In all cases we discover completely new (at least to this author) phenomena. The author has tried to refrain from making specific conjectures, inviting the reader, instead, to meditate on the data.