Haslegrave, J. and Jordan, J. (2018) Non-convergence of proportions of types in a preferential attachment graph with three co-existing types. Electronic Communications in Probability, 23. 54. ISSN 1083-589X
Abstract
We consider the preferential attachment model with multiple vertex types introduced by Antunovi ́c, Mossel and R ́acz. We give an example with three types, based on the game of rock-paper-scissors, where the proportions of vertices of the different types almost surely do not converge to a limit, giving a counterexample to a conjecture of Antunovi ́c, Mossel and R ́acz. We also consider another family of examples where we show that the conjecture does hold.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Institute of Mathematical Statistics. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | preferential attachment; stochastic approximation; social networks; competing types |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Aug 2018 09:53 |
Last Modified: | 01 Oct 2018 14:18 |
Published Version: | https://doi.org/10.1214/18-ECP157 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Refereed: | Yes |
Identification Number: | 10.1214/18-ECP157 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133860 |