Axelrod's Model in Two Dimensions

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Date

2014

Authors

Li, Junchi

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Durrett, Rick

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Abstract

In 1997 R. Axelrod introduced a model in which individuals have one of $Q$ possible opinions about each of $F$ issues and neighbors interact at a rate proportional to the fraction of opinions they share. Thanks to work by Lanchier and collaborators there are now a number of results for the one dimensional model. Here, we consider Axelrod's model on a square subset of the two-dimensional lattice start from a randomly chosen initial state and simplify things by supposing that $Q$ and $F$ large. If $Q/F$ is large then most neighbors have all opinions different and do not interact, so by a result of Lanchier the system soon reaches a highly disordered absorbing state. In contrast if $Q/F$ is small, then there is a giant component of individuals who share at least one opinion. In this case we show that consensus develops on this percolating cluster.

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Citation

Li, Junchi (2014). Axelrod's Model in Two Dimensions. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/8783.

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