13 papers
Loop vs. Bernoulli percolation on trees: strict inequality of critical values
Andreas Klippel, Benjamin Lees, Christian Mönch
We study loop ensembles on locally finite rooted trees. The loops are induced by a Poisson process of links on the edges; the transposition-only case is the random interchange proc…
Conditionally Poissonian random digraphs
Christian Mönch
We define a Poissonian model of directed random graphs which generalises the undirected Poissonian random graph process introduced by Norros and Reittu in Adv. Appl. Probab. 38 (20…
The one-point Schreier Poisson boundary of Thompson's group
Christian Mönch
We identify the Poisson boundary of the one-point Schreier-chain random walk obtained by projecting the simple symmetric random walk on Thompson's group to the dyadic orbit poi…
Phase transitions for contact processes on sparse random graphs via metastability and local limits
Benedikt Jahnel, Lukas Lüchtrath, Christian Mönch
We propose a new perspective on the asymptotic regimes of fast and slow extinction in the contact process on locally converging sequences of sparse finite graphs. We characterise t…
Partial orders and monotonicity of logarithmic depth and height in preferential attachment trees
Christian Mönch
We study preferential attachment (PA) trees with general attachment functions. PA suggests an intuitive monotonicity: if high-degree vertices are rewarded more strongly, then the r…
The mean field stubborn voter model
Lisa Hartung, Christian Mönch
We analyse the effect of agent-dependent heavy-tailed waiting times in the voter model on the complete graph with vertices. We derive a novel scaling limit and show the existen…