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Unperturbed Schelling segregation in two or three dimensions

Barmpalias, George, Elwes, Richard and Lewis-Pye, Andrew (2016) Unperturbed Schelling segregation in two or three dimensions. Journal of Statistical Physics, 164 (6). pp. 1460-1487. ISSN 0022-4715

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Identification Number: 10.1007/s10955-016-1589-6


Schelling's models of segregation, first described in 1969 [18] are among the best known models of self-organising behaviour. Their original purpose was to identify mechanisms of urban racial segregation. But his models form part of a family which arises in statistical mechanics, neural networks, social science, and beyond, where populations of agents interact on networks. Despite extensive study, unperturbed Schelling models have largely resisted rigorous analysis, prior results generally focusing on variants in which noise is introduced into the dynamics, the resulting system being amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory [25]. A series of recent papers [6, 3, 4], has seen the first rigorous analyses of 1-dimensional unperturbed Schelling models, in an asymptotic framework largely unknown in statistical mechanics. Here we provide the first such analysis of 2- and 3-dimensional unperturbed models, establishing most of the phase diagram, and answering a challenge from [6].

Item Type: Article
Official URL:
Additional Information: © 2016 Springer Science+Business Media New York
Divisions: Mathematics
Subjects: H Social Sciences > HT Communities. Classes. Races
Q Science > QA Mathematics
Date Deposited: 19 Jul 2016 16:49
Last Modified: 03 Jul 2024 20:45

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