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 functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D $\mathrm{XY}$ model. We demonstrate that this function describes the fluctuations of global quantities in other correlated equilibrium and nonequilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sandpiles, avalanches, and granular media in a self-organized critical state. We discuss the relationship with both Gaussian and extremal statistics.