Long-ranged correlations in large deviations of local clustering

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