Christian Hirsch

Feel free to have a look at my research interests

Preprints

• A Harris-Kesten theorem for confetti percolation pdf, arXiv 
  Percolation properties of the dead leaves model, also known as confetti percolation, are considered. More precisely, we prove that the critical probability for confetti percolation with square-shaped leaves is 1/2. This result is related to a question of Benjamini and Schramm concerning disk-shaped leaves and can be seen as a variant of the Harris-Kesten theorem for bond percolation. The proof is based on techniques developed by Bollob\'as and Riordan to determine the critical probability for Voronoi and Johnson-Mehl percolation.
  
  
• First-passage percolation on random geometric graphs and an application to shortest-path trees pdf
  joint with D. Neuhaeuser, C. Gloaguen and V. Schmidt
  We consider Euclidean first-passage percolation on a family of connected fibre processes in the d-dimensional Euclidean space. In particular, we establish a strong linear growth property for shortest-path (geodesic) lengths on fiber processes which are generated by point processes.  Our linear growth property implies a shape theorem for the Euclidean first-passage model defined by such fiber processes. Finally this shape theorem can be used to investigate a problem which is considered in structural analysis of fixed-access telecommunication networks.
  
  
• Prediction of regionalized car insurance risks based on control variates pdf
  joint with M. C. Christiansen and V. Schmidt
  We show how regional prediction of car insurance risks can be improved by combining explanatory modeling with phenomenological models from industrial practice. We also discuss how a non-parametric random forest approach may be used to practically compute such predictors and consider an application to German car insurance data.

Work in progress

• First-passage percolation on random geometric graphs and an application to shortest-path trees
  Joint with G.W. Delaney and V. Schmidt
• Moderate deviations for shortest-path lengths on random geometric graphs
  joint with D. Neuhaeuser and V. Schmidt