Two phase transitions for the contact process on small worlds

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In our version of Watts and Strogatz's small world model, space is a d-dimensional torus in which each individual has in addition exactly one long-range neighbor chosen at random from the grid. This modification is natural if one thinks of a town where an individual's interactions at school, at work, or in social situations introduce long-range connections. However, this change dramatically alters the behavior of the contact process, producing two phase transitions. We establish this by relating the small world to an infinite "big world" graph where the contact process behavior is similar to the contact process on a tree. We then consider the contact process on a slightly modified small world model in order to show that its behavior is decidedly different from that of the contact process on a tree. (c) 2007 Elsevier B.V. All rights reserved
Publisher
ELSEVIER SCIENCE BV
Issue Date
2007-12
Language
English
Article Type
Article
Citation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, v.117, no.12, pp.1910 - 1927

ISSN
0304-4149
DOI
10.1016/j.spa.2007.03.003
URI
http://hdl.handle.net/10203/213195
Appears in Collection
MA-Journal Papers(저널논문)
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