Mathematics Colloquium - Daniel Willhalm, University of Groningen

Title: Limit theory for spatial random networks

Abstract:

This talk deals with the asymptotic behavior of spatial random networks. Such networks can be modeled by arranging nodes randomly in a metric space and establishing connections based on spatial constraints or probabilities. Based on these networks it is possible to derive statistics such as edge lengths, subgraph counts or Betti numbers. This talk is concerned with the behavior of such statistics for various types of spatial networks and in particular, deals with the analysis of rare events. Rare events identified by a relatively small deviation from what is expected are the territory of central limit theorems. Rarer events can be approached with Poisson approximations or the theory of large deviations. The latter is the main focus of this talk.