Barmpalias, G, Elwes, R and Lewis-Pye, A (2016) Unperturbed Schelling Segregation in Two or Three Dimensions. Journal of Statistical Physics, 164 (6). pp. 1460-1487. ISSN 0022-4715
Abstract
Schelling’s models of segregation, first described in 1969 (Am Econ Rev 59:488–493, 1969) 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 (Young in Individual strategy and social structure: an evolutionary theory of institutions, Princeton University Press, Princeton, 1998). A series of recent papers (Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012); Barmpalias et al. in: 55th annual IEEE symposium on foundations of computer science, Philadelphia, 2014, J Stat Phys 158:806–852, 2015), 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 Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, Springer Science+Business Media New York. This is an author produced version of a paper published in Journal of Statistical Physics. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via http://dx.doi.org/10.1007/s10955-016-1589-6 |
Keywords: | Schelling segregation; Algorithmic game theory; Complex systems; Non-linear dynamics; Ising model; Spin glass |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Jul 2016 10:30 |
Last Modified: | 27 Jul 2017 07:50 |
Published Version: | http://dx.doi.org/10.1007/s10955-016-1589-6 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10955-016-1589-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:102484 |