Multiplicative Processes and City Sizes
In this contribution, I address the function of multiplicative stochastic processes in modelling the occurrence of power-law city size distributions. As an explanation of the result of Zipf’s rank analysis, Simon’s model is presented in a mathematically elementary way, with a thorough discussion of the involved hypotheses. Emphasis is put on the flexibility of the model, as to its possible extensions and the relaxation of some strong assumptions. I point out some open problems regarding the prediction of the detailed shape of Zipf’s rank plots, which may be tackled by means of such extensions.
KeywordsWord Frequency Urban System Evolution Step Urban Settlement City Size
Unable to display preview. Download preview PDF.
- Gabaix X, Ioannides Y (2004) The Evolution of City Size Distributions. In: Henderson V, Thisse JF (eds) Handbook of Urban and Regional Economics. Vol. 4, North-Holland, Amsterdam, pp 2341–2378Google Scholar
- Gibrat R (1931) Les inégalités économiques. Librairie du Recueil Sirey, ParisGoogle Scholar
- Montemurro MA, Zanette DH (2002) New perspectives on Zipf’s law in linguistic: From single textes to large corpora. Glottometrics 4: 86–98Google Scholar
- Portugali J (2000) Self-Organization and the City. Springer, BerlinGoogle Scholar
- Simon HA (1955) On a class of skew distribution functions. Biometrika 42: 425–440Google Scholar
- Sornette D (2000) Critical Phenomena in Natural Sciences. Chaos, Fractals, Selforganization and Disorder: Concepts and Tools. Springer, BerlinGoogle Scholar
- Willis J, Yule G (1922) Some statistics of evolution and geographical distribution in plants and animals, and their significance. Nature 109: 177Google Scholar
- Zanette DH (2006) Musicae Scientiae. In press, cs.CL/0406015.Google Scholar
- Zipf GK (1935) The Psycho-Biology of Language. Houghton-Mifflin, BostonGoogle Scholar
- Zipf GK (1949) Human Behaviour and the Principle of Least-Effort. Addison-Wesley, CambridgeGoogle Scholar