215 citations · 602 across the 30 of their papers we have counts for
33 papers
Inference by Multiple Identical Observers
Martin T. Barlow
We consider models for inference which involve observers which may have multiple copies, such as in the Sleeping Beauty problem. We establish a framework for describing these probl…
Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree
Martin T. Barlow, David A. Croydon, Takashi Kumagai
This article investigates the heat kernel of the two-dimensional uniform spanning tree. We improve previous work by demonstrating the occurrence of log-logarithmic fluctuations aro…
Stability of EHI and regularity of MMD spaces
Martin T. Barlow, Zhen-Qing Chen, Mathav Murugan
We show that elliptic Harnack inequality is stable under form-bounded perturbations for strongly local Dirichlet forms on complete locally compact separable metric spaces that sati…
A branching process with contact tracing
M. T. Barlow
We consider a supercritical branching process and define a contact tracing mechanism on its genealogical tree. We calculate the growth rate of the post tracing process, and give co…
Stability of parabolic Harnack inequalities on metric measure spaces
M. T. Barlow, R. F. Bass, T. Kumagai
Let be a metric measure space with a local regular Dirichlet form. We give necessary and sufficient conditions for a parabolic Harnack inequality with global space-time s…
Boundary Harnack principle and elliptic Harnack inequality
Martin T. Barlow, Mathav Murugan
We prove a scale-invariant boundary Harnack principle for inner uniform domains over a large family of Dirichlet spaces. A novel feature of our work is that our assumptions are rob…