| dc.description.abstract |
<p>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.</p>
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