Density-dependent stochastic resetting: a large deviations framework for achieving target distributions over networks

We develop a framework for designing density-dependent stochastic resetting protocols to regulate distributions of random walkers on networks. Resetting mechanisms that depend on local densities induce correlations in otherwise non-interacting walkers. Our framework allows for the study of both transient trajectories and stationary properties and identifies resetting protocols that maximise the likelihood of homogeneous and, more generally, rare configurations of random walkers.