18 citations · 84 across the 30 of their papers we have counts for
34 papers
Percolation of terraces, and enhancements for the orthant model
Mark Holmes, Thomas S. Salisbury
We study a model of an i.i.d.~random environment in general dimensions , where each site is equipped with one of two environments. The model comes with a parameter whic…
The mean square displacement of random walk on the Manhattan lattice
Nicholas R. Beaton, Mark Holmes
We give an explicit formula for the mean square displacement of the random walk on the -dimensional Manhattan lattice after steps, for all and all dimensions .
Multi-purpose open-end monitoring procedures for multivariate observations based on the empirical distribution function
Mark Holmes, Ivan Kojadinovic, Alex Verhoijsen
We propose nonparametric open-end sequential testing procedures that can detect all types of changes in the contemporary distribution function of possibly multivariate observations…
Balanced Excited Random Walk in Two Dimensions
Omer Angel, Mark Holmes, Alejandro Ramírez
We give non-trivial upper and lower bounds on the range of the so-called Balanced Excited Random Walk in two dimensions, and verify a conjecture of Benjamini, Kozma and Schapira. T…
WARM percolation on a regular tree in the strong reinforcement regime
Christian Hirsch, Mark Holmes, Victor Kleptsyn
We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter which governs the strength of the reinforcement, and a collect…
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…