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We are interested in the global fluctuations of macroscopic properties such as the roughness of an interface, or the center of mass of a cluster.

In two dimensions, many experimental realisations focus on clusters (sometimes called droplets, islands, or aggregates). Clusters have fluctuating edges as observed in many different systems such as monolayer islands on crystal surfaces, domains in magnetic thin films, bacteria colonies, or droplets in turbulent liquid crystal films.

The usual determination of the universality class relies on the spatio-temporal analysis of edge fluctuations. This analysis is delicate
because it requires a refined tracking of the moving edge with large enough statistics to determine correlation functions, or Hurst (fractal) exponents. We have proposed a novel measurement which is much simpler to investigate: the diffusion of the cluster center of mass. We show that this quantity exhibits a characteristic behavior which may be used to determine the universality class of edge fluctuations.

More precisely, the mean square displacement of the center of mass, which is known to behave linearly with time t in equilibrium, will for example behave as ln(t) in growth within the Edwards-Wilkinson universality class (close-to-equilibrium), and as t^1/3 within the Kardar-Parisi-Zhang universality class (far-from-equilibrium). We have also investigated the case of cluster evaporation