**Continuum percolation for Cox point processes**arXiv

joint with B. Jahnel and E. Cali

We investigate continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. First, we derive sufficient conditions for the existence of non-trivial sub- and super-critical percolation regimes based on the notion of stabilization. Second, we give asymptotic expressions for the percolation probability in large-radius, high-density and coupled regimes. In some regimes, we find universality, whereas in others, a sensitive dependence on the underlying random intensity measure survives.**Large deviations for the capacity in dynamic spatial relay networks**arXiv

joint with B. Jahnel

We derive a large deviation principle for the space-time evolution of users in a relay network that are unable to connect due to capacity constraints. The users are distributed according to a Poisson point process with increasing intensity in a bounded domain, whereas the relays are positioned deterministically with given limiting density. The preceding work on capacity for relay networks by the authors describes the highly simplified setting where users can only enter but not leave the system. In the present manuscript we study the more realistic situation where users leave the system after a random transmission time. For this we extend the point process techniques developed in the preceding work thereby showing that they are not limited to settings with strong monotonicity properties.

- M. Heydenreich, C. Hirsch and D. Valesin, Uniformity of hitting times of the contact process (arXiv). Latin American Journal of Probability and Statistics (2018), to appear.
- C. Hirsch, B. Jahnel and R.I.A. Patterson, Space-time large deviations in capacity-constrained relay networks (arXiv). Latin American Journal of Probability and Statistics (2018), to appear.
- D. Coupier and C. Hirsch, Coalescence of Euclidean geodesics on the Poisson-Delaunay triangulation. Bernoulli (2018), to appear.
- C. Hirsch, B. Jahnel, P. Keeler and R.I.A. Patterson, Large deviations in relay-augmented wireless networks. Queueing Systems (2018), to appear.
- C. Hirsch and G. Last, On maximal hard-core thinnings of stationary particle processes. Journal of Statistical Physics 170 (2018), 554-583.
- C. Hirsch, Tim Brereton and Volker Schmidt, Percolation and convergence properties of graphs related to minimal spanning forests. Electronic Journal of Probability 22 (2017), paper no. 105, 1-21.
- C. Hirsch, B. Jahnel, P. Keeler and R.I.A. Patterson, Traffic flow densities in large transport networks. Advances in Applied Probability 49 (2017), 1091-1115.
- C. Hirsch, From heavy-tailed Boolean models to scale-free Gilbert graphs. Brazilian Journal of Probability and Statistics 31 (2017), 111-143.
- C. Hirsch, B. Jahnel, P. Keeler and R.I.A. Patterson, Large-deviation principles for connectable receivers. Advances in Applied Probability 48 (2016), 1061-1094.
- C. Hirsch, D. Neuhäuser and V. Schmidt, Moderate deviations for shortest-path lengths on random segment processes. ESAIM: Probability and Statistics 20 (2016), 261-292.
- C. Hirsch, Bounded-hop percolation and wireless communication. Journal of Applied Probability 53 (2016), 833-845.
- D. Neuhäuser, C. Hirsch, C. Gloaguen and V. Schmidt, A stochastic model for multi-hierarchical networks. Methodology and Computing in Applied Probability 18 (2016), 1129-1151.
- C. Hirsch, On the absence of percolation in a line-segment based lilypond model. (arXiv). Annales de l’Institut Henri Poincaré 52 (2016), 127-145.
- C. Hirsch, G. W. Delaney and V. Schmidt, Stationary Apollonian packings. Journal of Statistical Physics 161 (2015), 35-72.
- C. Hirsch, D. Neuhäuser, C. Gloaguen and V. Schmidt, Asymptotic properties of Euclidean shortest-path trees in random geometric graphs. Statistics and Probability Letters 107 (2015), 122-130.
- C. Hirsch, G. Gaiselmann and V. Schmidt, Asymptotic properties of collective-rearrangement algorithms. ESAIM: Probability and Statistics 19 (2015), 236-250.
- C. Hirsch, D. Neuhaeuser, C. Gloaguen and V. Schmidt, First-passage percolation on random geometric graphs and an application to shortest-path trees. Advances in Applied Probability 47 (2015), 328-354.
- D. Neuhaeuser, C. Hirsch, C. Gloaguen and V. Schmidt, Joint distributions for total lengths of shortest-path trees in telecommunication networks. Annals of Telecommunications 70 (2015), 221-232.
- C. Hirsch, A Harris-Kesten theorem for confetti percolation. (arXiv). Random Structures & Algorithms 47 (2015), 361-385.
- D. Neuhaeuser, C. Hirsch, C. Gloaguen and V. Schmidt, Parametric modelling of sparse random trees using 3D copulas. Stochastic Models 31 (2015), 226-260.
- T. Brereton, C. Hirsch, V. Schmidt and D. Kroese, A critical exponent for shortest-path scaling in continuum percolation. Journal of Physics A: Mathematical and Theoretical 47 (2014), 505003--505014.
- 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. 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. 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. 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. 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. Queueing Systems 71 (2012), 199-220.

- R. Shah, C. Hirsch, D.P. Kroese and V. Schmidt, Rare event probability estimation for connectivity of large random graphs. 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. 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.