Fabiano L. Ribeiro, Diego Rybski

Physics Reports

Volume 1012, 23 April 2023, Pages 1-39

The quest for a theory of cities that could offer a quantitative and systematic approach to managing cities represents a top priority. If such a theory is feasible, then its formulation must be in a mathematical way. As a contribution to organizing the mathematical ideas that deal with such a systematic way of understanding urban phenomena, we review the main theoretical models present in the literature that aim at explaining the origin and emergence of urban scaling. We intend to present the models, identify similarities and connections between them, and find situations in which different models lead to the same output. In addition, we report situations where some ideas initially introduced in a particular model can also be introduced in another one, generating more diversification and increasing the scope of the original works. The models treated…