First-passage times of many persistent random walkers in higher dimensions

The field of active matter studies particles, or collections thereof, which consume energy to perform motion. This defining property's main consequence is the breaking of detailed balance: active systems are inherently out of equilibrium, and as such cannot be described by the Boltzmann distribution. With a general framework of non-equilibrium statistical mechanics lacking, active-matter models serve as an effective means by which we can develop our intuition for the former.

Originally inspired by Escherichia coli bacteria, one such set of models which have been heavily studied are run-and-tumble models. While much analytical work has been conducted at a field-theoretic level, almost all microscopic, interacting run-and-tumble models are limited in particle number and are restricted to one dimension. Here, we will first lift the latter restriction by presenting an approximate solution to a two-particle first-passage problem in two dimensions. We will then extend this approach by generalising to N dilute particles in d dimensions, and present evidence for clustering behaviour even at very low densities.