Spectral experiments+

Igor Rivin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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 frommaking specific conjectures, inviting the reader, instead, to meditate on the data.

Original languageEnglish
Pages (from-to)379-388
Number of pages10
JournalExperimental Mathematics
Volume25
Issue number4
DOIs
Publication statusPublished - 30 Mar 2016

Keywords

  • Delaunay tessellations
  • GOE
  • Localization
  • Random matrices
  • Random point sets
  • Random triangulations
  • Voronoi diagrams

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