Communications in Mathematical Sciences

Volume 14 (2016)

Number 2

Exploring the effects of social preference, economic disparity, and heterogeneous environments on segregation

Pages: 363 – 387



Nancy Rodríguez (Department of Mathematics, University of North Carolina, Chapel Hill, N.C., U.S.A.)

Lenya Ryzhik (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)


It is believed that social preference, economic disparity, and heterogeneous environments are mechanisms that lead to segregation. However, it is difficult to unravel the exact role of each mechanism in a complex social system. We introduce a versatile, simple and intuitive particle-interaction model that allows one to separate the effect of each of these factors. As the population size and number of groups with different economic status approach infinity, we derive various macroscopic models for the population density. Through the analysis of the continuous limits, we conclude that, within this range of models, social preference is a necessary but not always sufficient mechanism for segregation. On the other hand, when combined with the environment and economic disparity (which on the their own also do not cause segregation), social preference does enhance segregation.


parabolic system, degenerate diffusion, non-local interactions, particle-interaction model

2010 Mathematics Subject Classification

35K55, 35K57, 35K65, 35Q92

Published 14 December 2015