Weak shape theorem in first passage percolation with infinite passage times

Abstract : We consider the model of i.i.d. first passage percolation on $\mathbb{Z}^d$ : we associate with each edge $e$ of the graph a passage time $t(e)$ taking values in $[0,+\infty]$, such that $\mathbb{P}[t(e)<+\infty] >p_c(d)$. Equivalently, we consider a standard (finite) i.i.d. first passage percolation model on a super-critical Bernoulli percolation performed independently. We prove a weak shape theorem without any moment assumption. We also prove that the corresponding time constant is positive if and only if $\mathbb{P}[t(e)=0]
Type de document :
Pré-publication, Document de travail
34 pages, 4 figures. 2014
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https://hal.archives-ouvertes.fr/hal-00980479
Contributeur : Marie Théret <>
Soumis le : vendredi 18 avril 2014 - 09:58:34
Dernière modification le : mercredi 4 janvier 2017 - 16:22:45

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  • HAL Id : hal-00980479, version 1
  • ARXIV : 1404.4539

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Citation

Raphaël Cerf, Marie Théret. Weak shape theorem in first passage percolation with infinite passage times. 34 pages, 4 figures. 2014. <hal-00980479>

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