Minority population in the one-dimensional Schelling model of segregation

Barmpalias, George, Elwes, Richard and Lewis-Pye, Andy (2018) Minority population in the one-dimensional Schelling model of segregation. Journal of Statistical Physics. ISSN 0022-4715

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Abstract

The Schelling model of segregation looks to explain the way in which a population of agents or particles of two types may come to organise itself into large homogeneous clusters, and can be seen as a variant of the Ising model in which the system is subjected to rapid cooling. While the model has been very extensively studied, the unperturbed (noiseless) version has largely resisted rigorous analysis, with most results in the literature pertaining to versions of the model in which noise is introduced into the dynamics so as to make it 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 by Brandt, Immorlica, Kamath, and Kleinberg.

Item Type:	Article
Official URL:	https://link.springer.com/journal/10955
Additional Information:	© 2018 Elsevier B.V.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	03 Sep 2018 08:56
Last Modified:	29 Mar 2024 02:48
Projects:	2010Y2GB03, 2014CB340302
Funders:	1000 Talents Program for Young Scholars from the Chinese Government, Chinese Academy of Sciences, Marsden grant of New Zealand, China Basic Research Program, Royal Society University Research Fellowship
URI:	http://eprints.lse.ac.uk/id/eprint/90163

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