Long-ranged correlations in large deviations of local clustering

In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realise large-deviation events. The bias acts on a single particle, but elicits a response that spans the whole system. We analyse this effect through the lens of Macroscopic Fluctuation Theory, focussing on the coupling of the bias to hydrodynamic modes. This explains that the dynamical free energy has non-trivial scaling relationships with the system size, in 1 and 2 spatial dimensions. We show that the long-ranged response to a bias on one particle also has consequences when biasing two particles.