4 papers
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…
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…