M. Holmes

activity

20082025

most citedMonotonicity for excited random walk in high dimensions

1 citations · 1 across the 3 of their papers we have counts for

collaborators

4 papers

math.PR2025

Coalescence in Markov chains

Geoffrey R. Grimmett, Mark Holmes

A Markov chain $X^{i}$ on a finite state space $S$ has transition matrix $P$ and initial state $i$ . We may run the chains $(X^{i} : i \in S)$ in parallel, while insisting that any two su…

math.PR2025

Random skeletons in high-dimensional lattice trees

Manuel Cabezas, Alexander Fribergh, Mark Holmes +1

We study the behaviour of the rescaled minimal subtree containing the origin and K random vertices selected from a random critical (sufficiently spread-out, and in dimensions d > 8…

math.PR2024

Chemical distance for the half-orthant model

Nicholas Beaton, Mark Holmes, Xin Huang

The half-orthant model is a partially oriented model of a random medium involving a parameter $p \in [0, 1]$ , for which there is a critical value $p_{c} (d)$ (depending on the dimension…

math.PR2008★ 1 cited

Monotonicity for excited random walk in high dimensions

Remco van der Hofstad, Mark Holmes

We prove that the drift $θ (d, β)$ for excited random walk in dimension $d$ is monotone in the excitement parameter $β \in [0, 1]$ , when $d \geq 9$ .