Publications (40)
A shape theorem for the orthant model
Mark Holmes, Thomas S. Salisbury
We study a particular model of a random medium, called the orthant model, in general dimensions . Each site independently has arrows pointing to its positive ne…
An extension of the inductive approach to the lace expansion
Remco van der Hofstad, Mark Holmes, Gordon Slade
We extend the inductive approach to the lace expansion, previously developed to study models with critical dimension 4, to be applicable more generally. In particular, the result o…
Strongly reinforced Pólya urns with graph-based competition
Remco van der Hofstad, Mark Holmes, Alexey Kuznetsov +1
We introduce a class of reinforcement models where, at each time step , one first chooses a random subset of colours (independent of the past) from colours of balls, a…
Open-end nonparametric sequential change-point detection based on the retrospective CUSUM statistic
Mark Holmes, Ivan Kojadinovic
The aim of online monitoring is to issue an alarm as soon as there is significant evidence in the collected observations to suggest that the underlying data generating mechanism ha…
The voter model chordal interface in two dimensions
Mark Holmes, Yevhen Mohylevskyy, Charles M. Newman
Consider the voter model on a box of side length (in the triangular lattice) with boundary votes fixed forever as type 0 or type 1 on two different halves of the boundary. Moti…
Coalescence in Markov chains
Geoffrey R. Grimmett, Mark Holmes
A Markov chain on a finite state space has transition matrix and initial state . We may run the chains in parallel, while insisting that any two su…