4 citations · 8 across the 5 of their papers we have counts for
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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…