Universal Fluctuations of the Danube Water Level : a Link with Turbulence , Criticality and Company Growth

– A global quantity, regardless of its precise nature, will often fluctuate according to a Gaussian limit distribution. However, in highly correlated systems, other limit distributions are possible. We have previously calculated one such distribution and have argued that this function should apply specifically, and in many instances, to global quantities that define a steady state [1]. Here we demonstrate, for the first time, the relevance of this prediction to natural phenomena. The river level fluctuations of the Danube [2] are observed to obey our prediction, which immediately establishes a generic statistical connection between turbulence, criticality and company growth statistics. Jánosi and Gallas have analysed statistics of the daily water level fluctuations of the Danube collected over the major part of the 20 century [2]. In Figure 1 we show their histogram P (h) of seasonally adjusted river height fluctuations. The data are plotted in the form σP against (