The generalized central limit theorem and Lévy stable laws

Abstract

Abstract Before developing other models of urban growth that include interurban migration flows, a few more mathematical results are necessary. In this chapter, we will start with a very common probabilistic result, the central limit theorem, and introduce its generalization. This will help us to define the so-called Lévy stable laws, which are typical “broad laws”: laws that describe large but rare events. These laws obey their own rules and will be paramount in the further description of migrations flows. Indeed, we will see in Chapter 9 that interurban migrations flows are actually dominated by rare, but large events.