4 citations · 8 across the 13 of their papers we have counts for
5 papers · 2 filters
Extremal life times of persistent loops and holes
Nicolas Chenavier, Christian Hirsch
Persistent homology captures the appearances and disappearances of topological features such as loops and holes when growing disks centered at a Poisson point process. We study ext…
WARM percolation on a regular tree in the strong reinforcement regime
Christian Hirsch, Mark Holmes, Victor Kleptsyn
We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter which governs the strength of the reinforcement, and a collect…
Rare Events in Random Geometric Graphs
Christian Hirsch, Sarat B. Moka, Thomas Taimre +1
This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the…
Extremal linkage networks
Markus Heydenreich, Christian Hirsch
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Ev…
Optimal stationary markings
Bartłomiej Błaszczyszyn, Christian Hirsch
Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tu…