Condensation in random geometric graphs

• Applicant: Professor Dr. Peter Mörters
• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444092244

The project we propose is a continuation of the project of the same name in the first funding period. In both parts of the project we explore the condensation phenomena arising when a geometric random graph is conditioned on certain unlikely events. The first part of the project was focused on the event of the graph having exceptionally many edges, in which case the condensation can manifest itself in the emergence of vertices with exceptionally high degree or of localized clusters of exceptionally high connectivity. In the second part our principal aim is to extend this work to more general large deviation events, for example the graph having unusually many triangles, untypically long paths or large connected components. These events are also based on a condensation effect, which we will explore in greater depth. We will also use and extend recent new methods developed in the analysis of sharp phase transitions in geometric random graphs and other percolation models.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2265: Random geometric systems