Mark Holmes

The Continuous-Time Lace Expansion

David Brydges, Tyler Helmuth, Mark Holmes

Journal article  |  2021  |  COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

We derive a continuous-time lace expansion for a broad class of self-interacting continuous-time random walks. Our expansion appli..

A SHAPE THEOREM FOR THE ORTHANT MODEL

Mark Holmes, Thomas S Salisbury

Journal article  |  2021  |  ANNALS OF PROBABILITY

Alignment Percolation

Nicholas R Beaton, Geoffrey R Grimmett, Mark Holmes

Journal article  |  2021  |  MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY

The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in d≥ 2 dimensions..

ABSENCE OF WARM PERCOLATION IN THE VERY STRONG REINFORCEMENT REGIME

Christian Hirsch, Mark Holmes, Victor Kleptsyn

Journal article  |  2021  |  ANNALS OF APPLIED PROBABILITY

We study a class of reinforcement models involving a Poisson process on the vertices of certain infinite graphs G. When a vertex f..

Phase transitions for degenerate random environments

Mark Holmes, Thomas S Salisbury

Journal article  |  2021  |  ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS

Non-Coupling from the Past

Geoffrey R Grimmett, Mark Holmes

Book Chapter  |  2021

Open-end nonparametric sequential change-point detection based on the retrospective CUSUM statistic

Mark Holmes, Ivan Kojadinovic

Journal article  |  2021  |  ELECTRONIC JOURNAL OF STATISTICS

The aim of online monitoring is to issue an alarm as soon as there is significant evidence in the collected observations to sugges..

CURIOSITIES REGARDING WAITING TIMES IN POLYA'S URN MODEL

Norbert Henze, Mark Holmes

Journal article  |  2020  |  Transactions of A. Razmadze Mathematical Institute

Consider an urn, initially containing b black and w white balls. Select a ball at random and observe its colour. If it is black, s..

On the range of lattice models in high dimensions

Mark Holmes, Edwin Perkins

Journal article  |  2020  |  PROBABILITY THEORY AND RELATED FIELDS

We investigate the scaling limit of the range (the set of visited vertices) for a general class of critical lattice models, starti..

Biased Random Walk on the Trace of Biased Random Walk on the Trace of ...

David Croydon, Mark Holmes

Journal article  |  2020  |  COMMUNICATIONS IN MATHEMATICAL PHYSICS

We study the behaviour of a sequence of biased random walks (X(i))i≥0 on a sequence of random graphs, where the initial graph is Z..