I have moved to WIAS Berlin
- Stationary Apollonian packings pdf
joint with G. W. Delaney and V. Schmidt
The notion of stationary Apollonian packings in the d-dimensional Euclidean space is introduced as a mathematical formalization of so-called random Apollonian packings and rotational random Apollonian packings, which constitute popular grain packing models in physics. Apart from dealing with issues of existence and uniqueness in the entire Euclidean space, asymptotic results are provided for the growth durations and it is shown that the packing is space-filling with probability 1, in the sense that the Lebesgue measure of its complement is zero. Finally, the phenomenon is studied that grains arrange in clusters and properties related to percolation are investigated.
Publications in Journals
- D. Neuhaeuser, C. Hirsch, C. Gloaguen and V. Schmidt, Parametric modelling of sparse random trees using 3D copulas. (pdf). Stochastic Models (to appear).
- C. Hirsch, G. Gaiselmann and V. Schmidt, Asymptotic properties of collective-rearrangement algorithms. (pdf). ESAIM: Probability and Statistics (to appear).
- C. Hirsch, On the absence of percolation in a line-segment based lilypond model. (arXiv). Annales de l’Institut Henri Poincaré (to appear).
- C. Hirsch, D. Neuhaeuser, C. Gloaguen and V. Schmidt, First-passage percolation on random geometric graphs and an application to shortest-path trees. (pdf). Advances in Applied Probability (to appear).
- C. Hirsch, A Harris-Kesten theorem for confetti percolation. (arXiv). Random Structures & Algorithms (to appear).
- D. Neuhaeuser, C. Hirsch, C. Gloaguen and V. Schmidt, Joint distributions for total lengths of shortest-path trees in telecommunication networks. (pdf). Annals of Telecommunications (to appear)
- T. Brereton, C. Hirsch, V. Schmidt and D. Kroese, A critical exponent for shortest-path scaling in continuum percolation (pdf). Journal of Physics A: Mathematical and Theoretical 47 (2014), 505003.
- O. Stenzel, C. Hirsch, V. Schmidt, T. Brereton, D.P. Kroese, B. Baumeier and D. Andrienko, A general framework for consistent estimation of charge transport properties via random walks in random environments (pdf). Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 12 (2014), 1108-1134.
- M. C. Christiansen, C. Hirsch and V. Schmidt, Prediction of regionalized car insurance risks based on control variates (pdf). Statistics & Risk Modeling 31 (2014), 163-181
- D. Neuhaeuser, C. Hirsch, C. Gloaguen and V. Schmidt, Ratio limits and simulation algorithms for the Palm version of stationary iterated tessellations (pdf). Journal of Statistical Computation and Simulation 84 (2014), 1486-1504
- C. Hirsch, D. Neuhaeuser, and V. Schmidt, Connectivity of random geometric graphs related to minimal spanning forests (pdf). Advances in Applied Probability 45 (2013), 20-36.
- D. Neuhaeuser, C. Hirsch, C. Gloaguen and V. Schmidt, On the distribution of typical shortest-path lengths in connected random geometric graphs (pdf). Queueing Systems 71 (2012), 199-220.
Publications in Conference Proceedings
- R. Shah, C. Hirsch, D.P. Kroese and V. Schmidt, Rare event probability estimation for connectivity of large random graphs (pdf). Proceedings of the 2014 Winter Simulation Conference, A Tolks, S.D. Diallo, I.O, Ryzhov, L. Yilmaz, S. Buckley, and J.A. Miller, eds
- D. Neuhaeuser, C. Hirsch, C. Gloaguen and V. Schmidt, A parametric copula approach for modelling shortest-path trees in telecommunication networks (pdf). In: A. Dudin and K. Turck (eds.) Analytical and Stochastic Modeling Techniques and Applications. Lecture Notes in Computer Science 7984, Springer, Berlin 2013, 324-336.