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Résumé |
The most fundamental problem for constructing a science of cities is to
understand the hierarchical organization of city population and the
statistical occurrence of megacities. This was first thought to be described
by a universal principle known since almost a century as Zipf's law.
However, the validity of this model has been challenged by recent empirical
studies. In addition, a theoretical model must also be able to explain the
rises and falls of cities and civilizations. Despite many attempts that I
will briefly review here (the Gibrat and Gabaix models), these fundamental
questions have not yet been satisfactorily answered. In this talk, starting
from an empirical analysis of recent datasets (for Canada, France, the UK
and the USA) I will derive a stochastic equation with multiplicative noises
for modelling population growth in cities. This model reveals how rare, but
large, interurban migratory shocks dominate city growth and predicts a
complex shape for the distribution of city population. It also shows that,
owing to finite-time effects, Zipf's law does not hold in general, implying
a more complex organization of cities. It also predicts the existence of
multiple temporal variations in the city hierarchy, in agreement with
empirical observations. \\ \\ Reference: V. Verbavatz, M. Barthelemy, "The
growth equation of cities", Nature 587, 397-401 (2020). \\ \\ The link to
attend the talk on-line is: https://bbb.ipht.fr/b/mar-x7f-nkk |
