Barmpalias, G, Elwes, R and Lewis-Pye, A (2018) Minority population in the one-dimensional Schelling model of segregation. Journal of Statistical Physics, 173 (5). pp. 1408-1458. ISSN 0022-4715
Abstract
Schelling models of segregation attempt to explain how a population of agents or particles of two types may organise itself into large homogeneous clusters. They can be seen as variants of the Ising model. While such models have been extensively studied, unperturbed (or noiseless) versions have largely resisted rigorous analysis, with most results in the literature pertaining models in which noise is introduced, so as to make them amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. We rigorously analyse the one-dimensional version of the model in which one of the two types is in the minority, and establish various forms of threshold behaviour. Our results are in sharp contrast with the case when the distribution of the two types is uniform (i.e. each agent has equal chance of being of each type in the initial configuration), which was studied in Brandt et al. (in: STOC ’12: proceedings of the 44th symposium on theory of computing, pp. 789–804, 2012) and Barmpalias et al. (in: 55th Annual IEEE symposium on foundations of computer science, Oct 18–21, Philadelphia, FOCS’14, 2014).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Schelling segregation; Minority population; Phase diagram |
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: | 31 Aug 2018 11:46 |
Last Modified: | 25 Jun 2023 21:29 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10955-018-2146-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:135145 |