Extended Data Fig. 9: Microdynamics of city rank through time for the largest cities in France, the USA and the UK.
Data is given for the 500 largest cities in France between 1875 and 2016 (top), the 100 largest cities in the United States between 1790 and 1990 (middle) and the 40 largest cities in the UK between 1861 and 1991 (bottom). The left panels display the right-cumulative distribution of the maximal variation of the rank ri(t) for city, that is, the difference between the highest and the lowest rank in population for each city. The right panels display the typical fluctuations of the rank ri(t) through time. In the three cases, the Lévy model is able to predict rare but non-negligible large variations of rank such as the sudden birth or death of city, in contrast to Gabaix’s model or Gibrat’s model for growth, for which large fluctuations of rank order do not occur.
