4 citations · 8 across the 5 of their papers we have counts for
7 papers
The Direct-Connectedness Function in the Random Connection Model
Sabine Jansen, Leonid Kolesnikov, Kilian Matzke
We investigate expansions for connectedness functions in the random connection model of continuum percolation in powers of the intensity. Precisely, we study the pair-connectedness…
Expansion for the critical point of site percolation: the first three terms
Markus Heydenreich, Kilian Matzke
We expand the critical point for site percolation on the -dimensional hypercubic lattice in terms of inverse powers of , and we obtain the first three terms rigorously. This…
Critical site percolation in high dimension
Markus Heydenreich, Kilian Matzke
We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive…
Lace Expansion and Mean-Field Behavior for the Random Connection Model
Markus Heydenreich, Remco van der Hofstad, Günter Last +1
We study the random connection model driven by a stationary Poisson process. In the first part of the paper, we derive a lace expansion with remainder term in the continuum and bou…
Phase transition for a non-attractive infection process in heterogeneous environment
Marinus Gottschau, Markus Heydenreich, Kilian Matzke +1
We consider a non-attractive three state contact process on and prove that there exists a regime of survival as well as a regime of extinction. In more detail, the proc…
Reptilings and space-filling curves for acute triangles
Marinus Gottschau, Herman Haverkort, Kilian Matzke
An -gentiling is a dissection of a shape into parts which are all similar to the original shape. An -reptiling is an -gentiling of which all parts are mutually…
The Saturation Time of Graph Bootstrap Percolation
Kilian Matzke
The process of -bootstrap percolation for a graph is a cellular automaton, where, given a subset of the edges of as initial set, an edge is added at time if it is…