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If $(\omega(e))$ is a family of random variables (weights) assigned to the edges of $\mathbb{Z}^d$, the nearest neighbor graph is the directed graph induced by all edges $\langle x,y \rangle$ such that $\omega(\{x,y\})$ is minimal among all neighbors
Externí odkaz:
http://arxiv.org/abs/2006.16347
Autor:
Bock, Bounghun, Damron, Michael
Invasion percolation is a stochastic growth model that follows a greedy algorithm. After assigning i.i.d. uniform random variables (weights) to all edges of $\mathbb{Z}^d$, the growth starts at the origin. At each step, we adjoin to the current clust
Externí odkaz:
http://arxiv.org/abs/1904.08893
In independent bond percolation on $\mathbb{Z}^d$ with parameter $p$, if one removes the vertices of the infinite cluster (and incident edges), for which values of $p$ does the remaining graph contain an infinite cluster? Grimmett-Holroyd-Kozma used
Externí odkaz:
http://arxiv.org/abs/1811.01678
Akademický článek
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Autor:
Bock, Bounghun1 (AUTHOR), Damron, Michael1 (AUTHOR) mdamron6@gatech.edu, Newman, C. M.2,3 (AUTHOR), Sidoravicius, Vladas3 (AUTHOR)
Publikováno v:
Journal of Statistical Physics. May2020, Vol. 179 Issue 3, p789-807. 19p.
Publikováno v:
Fluctuation & Noise Letters. Mar2013, Vol. 12 Issue 1, p-1. 13p.