8 papers · 1 filter
On the rate of convergence in quenched Voronoi percolation
Daniel Ahlberg, Daniel de la Riva, Simon Griffiths
Position points uniformly at random in the unit square , and consider the Voronoi tessellation of corresponding to the set of points. Toss a fair coin for each cell…
To fixate or not to fixate in two-type annihilating branching random walks
Daniel Ahlberg, Simon Griffiths, Svante Janson
We study a model of competition between two types evolving as branching random walks on . The two types are represented by red and blue balls respectively, with the r…
Existence and coexistence in first-passage percolation
Daniel Ahlberg
We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of g…
Tertiles and the time constant
Daniel Ahlberg
We consider planar first-passage percolation and show that the time constant can be bounded by multiples of the first and second tertiles of the weight distribution. As a consequen…
The two-type Richardson model in the half-plane
Daniel Ahlberg, Maria Deijfen, Christopher Hoffman
The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity,…
Competing first passage percolation on random graphs with finite variance degrees
Daniel Ahlberg, Maria Deijfen, Svante Janson
We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at ran…