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Doctoral thesis
Open access
English

The Laplacian of the Erdős-Rényi graph

ContributorsRivier, Renaud
Number of pages183
Imprimatur date2023
Defense date2023
Abstract

This thesis studies the spectral properties of the Laplacian matrix of the Erdős-Rényi graph. Various results are proved including local law and eigenvector delocalization in the bulk of the spectrum as well as Poisson statistics and eigenvector localization at the edge of the spectrum.

eng
Keywords
  • Random matrices
  • Random graphs
  • Local law
  • Extreme eigenvalue statistics
Citation (ISO format)
RIVIER, Renaud. The Laplacian of the Erdős-Rényi graph. 2023. doi: 10.13097/archive-ouverte/unige:170196
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Technical informations

Creation07/16/2023 12:33:08 PM
First validation07/17/2023 9:10:06 AM
Update time07/17/2023 9:10:06 AM
Status update07/17/2023 9:10:06 AM
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