Corpus ID: 119318650

Asymptotic behavior of the Eden model with positively homogeneous edge weights

@article{Bubeck2015AsymptoticBO,
  title={Asymptotic behavior of the Eden model with positively homogeneous edge weights},
  author={S'ebastien Bubeck and Ewain Gwynne},
  journal={arXiv: Probability},
  year={2015}
}

S'ebastien Bubeck, Ewain Gwynne

Published 2015

Mathematics

arXiv: Probability

Let $d\in\mathbb N$, $\alpha\in\mathbb R$, and let $f :\mathbb R^d\setminus \{0\} \rightarrow (0,\infty)$ be locally Lipschitz and positively homogeneous of degree $\alpha$ (e.g. $f$ could be the $\alpha$th power of a norm on $\mathbb R^d$). We study a generalization of the Eden model on $\mathbb Z^d$ wherein the next edge added to the cluster is chosen from the set of all edges incident to the current cluster with probability proportional to the value of $f$ at the midpoint of this edge… CONTINUE READING

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