9 papers
High-degree vertices in uniform recursive directed acyclic graphs with freezing
Rafael Engel, Bas Lodewijks
We study uniform recursive directed acyclic graphs with freezing. Here, a graph is built by adding vertices one-by-one and connecting a new vertex to uniformly sele…
Preferential Attachment Trees with Vertex Death: Persistence of the Maximum Degree
Bas Lodewijks
We consider an evolving random discrete tree model called Preferential Attachment with Vertex Death, as introduced by Deijfen. Initialised with an alive root labelled , at each…
Local criteria for global connectivity comparisons: beyond stochastic domination
Johannes Bäumler, Benedikt Jahnel, Jonas Köppl +3
We introduce a site-wise domination criterion for local percolation models, which enables the comparison of one-arm probabilities even in the absence of stochastic domination. The…
On the depth of depth-weighted trees
Lyuben Lichev, Amitai Linker, Bas Lodewijks +1
The depth-weighted tree DWT() with weight function is a dynamic random tree grown from a root where vertices arrive consecutively and ever…
A star is born: Explosive Crump-Mode-Jagers branching processes
Bas Lodewijks
We study a family of Crump--Mode--Jagers branching processes in random environment that explode, i.e. that grow infinitely large in finite time with positive probability. Building…
Long-range competition on the torus
Bas Lodewijks, Neeladri Maitra
We study competition between two growth models with long-range correlations on the torus of size in dimension . We append the edge set of the torus $\mathbb…