Non-convergence of proportions of types in a preferential attachment graph with three co-existing types

John Haslegrave; Jonathan Jordan

doi:10.1214/18-ecp157

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arXiv · 1805.10071

Non-convergence of proportions of types in a preferential attachment graph with three co-existing types

John Haslegrave·Jonathan Jordan

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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.

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John Haslegrave, Jonathan Jordan. 2018-05-25. Non-convergence of proportions of types in a preferential attachment graph with three co-existing types. https://doi.org/10.1214/18-ecp157

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