Universal fluctuations in correlated systems

The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same function al form. Here, we identify the analytical form of the PDF of one such measu re. the order parameter in the low temperature phase of the 2D XY model. We demonstrate that this function describes the fluctuations of global quanti ties in other correlated equilibrium and nonequilibrium systems. These incl ude a coupled rotor model, Ising and percolation models, models of forest f ires, sandpiles, avalanches, and granular media in a self-organized critica l state. We discuss the relationship with both Gaussian and extremal statis tics.