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Non-convergence of proportions of types in a preferential attachment graph with three co-existing types
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Haslegrave, John and Jordan, Jonathan (2018) Non-convergence of proportions of types in a preferential attachment graph with three co-existing types. Electronic communications in probability, 23 . 54. doi:10.1214/18-ECP157 ISSN 1083-589X.
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Official URL: https://doi.org/10.1214/18-ECP157
Abstract
We consider the preferential attachment model with multiple vertex types introduced by Antunovi¢, Mossel and Rácz. 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¢, Mossel and Rácz. We also consider another family of examples where we show that the conjecture does hold.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Random graphs, Differential equations | ||||||
| Journal or Publication Title: | Electronic communications in probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 1083-589X | ||||||
| Official Date: | 1 September 2018 | ||||||
| Dates: |
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| Volume: | 23 | ||||||
| Number of Pages: | 12 | ||||||
| Article Number: | 54 | ||||||
| DOI: | 10.1214/18-ECP157 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 21 August 2018 | ||||||
| Date of first compliant Open Access: | 12 September 2018 | ||||||
| RIOXX Funder/Project Grant: |
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