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Register a new userUrban and Scientific Segregation: The Schelling-Ising Model
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Urban segregation of different communities, like blacks and whites in the USA, has been simulated by Ising-like models since Schelling 1971. This research was accompanied by a scientific segregation, with sociologists and physicists ignoring each other until 2000. We review recent progress and also present some new two-temperature multi-cultural simulations.
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In this work we characterize sudden increases in the land price of certain urban areas, a phenomenon causing gentrification, via an extended Schelling model. An initial price rise forces some of the disadvantaged inhabitants out of the area, creating vacancies which other groups find economically attractive. Intolerance issues forces further displacements, possibly giving rise to an avalanche. We consider how gradual changes in the economic environment affect the urban architecture through such avalanche processes, when agents may enter or leave the city freely. The avalanches are characterized by power-law histograms, as it is usually the case in self-organized critical phenomena.
The phenomenon of residential segregation was captured by Schellings famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same type as her is at least $tau$, for some $0<tau<1$. Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty cell. We analyze a generalized game-theoretic model of Schelling segregation which allows more than two agent types and more general underlying graphs modeling the residential area. For this we show that both aspects heavily influence the dynamic properties and the tractability of finding an optimal placement. We map the boundary of when improving response dynamics (IRD), i.e., the natural approach for finding equilibrium states, are guaranteed to converge. For this we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into the strongest possible non-convergence result: a violation of weak acyclicity. In particular, we show such threshold results also for Schellings original model, which is in contrast to the standard assumption in many empirical papers. Furthermore, we show that in case of convergence, IRD find an equilibrium in $mathcal{O}(m)$ steps, where $m$ is the number of edges in the underlying graph and show that this bound is met in empirical simulations starting from random initial agent placements.
Social networks amplify inequalities due to fundamental mechanisms of social tie formation such as homophily and triadic closure. These forces sharpen social segregation reflected in network fragmentation. Yet, little is known about what structural factors facilitate fragmentation. In this paper we use big data from a widely-used online social network to demonstrate that there is a significant relationship between social network fragmentation and income inequality in cities and towns. We find that the organization of the physical urban space has a stronger relationship with fragmentation than unequal access to education, political segregation, or the presence of ethnic and religious minorities. Fragmentation of social networks is significantly higher in towns in which residential neighborhoods are divided by physical barriers such as rivers and railroads and are relatively distant from the center of town. Towns in which amenities are spatially concentrated are also typically more socially segregated. These relationships suggest how urban planning may be a useful point of intervention to mitigate inequalities in the long run.
Urbanization has been the dominant demographic trend in the entire world, during the last half century. Rural to urban migration, international migration, and the re-classification or expansion of existing city boundaries have been among the major reasons for increasing urban population. The essentially fast growth of cities in the last decades urgently calls for a profound insight into the common principles stirring the structure of urban developments all over the world. We have discussed the graph representations of urban spatial structures and suggested a computationally simple technique that can be used in order to spot the relatively isolated locations and neighborhoods, to detect urban sprawl, and to illuminate the hidden community structures in complex urban textures. The approach may be implemented for the detailed expertise of any urban pattern and the associated transport networks that may include many transportation modes.
A version of the Schelling model on $mathbb{Z}$ is defined, where two types of agents are allocated on the sites. An agent prefers to be surrounded by other agents of its own type, and may choose to move if this is not the case. It then sends a request to an agent of opposite type chosen according to some given moving distribution and, if the move is beneficial for both agents, they swap location. We show that certain choices in the dynamics are crucial for the properties of the model. In particular, the model exhibits different asymptotic behavior depending on whether the moving distribution has bounded or unbounded support. Furthermore, the behavior changes if the agents are lazy in the sense that they only swap location if this strictly improves their situation. Generalizations to a version that includes multiple types are discussed. The work provides a rigorous analysis of so called Kawasaki dynamics on an infinite structure with local interactions.
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