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2018 Existence and continuity of the flow constant in first passage percolation
Raphaël Rossignol, Marie Théret
Electron. J. Probab. 23: 1-42 (2018). DOI: 10.1214/18-EJP214

Abstract

We consider the model of i.i.d. first passage percolation on $\mathbb{Z} ^d$, where we associate with the edges of the graph a family of i.i.d. random variables with common distribution $G$ on $ [0,+\infty ]$ (including $+\infty $). Whereas the time constant is associated to the study of $1$-dimensional paths with minimal weight, namely geodesics, the flow constant is associated to the study of $(d-1)$-dimensional surfaces with minimal weight. In this article, we investigate the existence of the flow constant under the only hypothesis that $G(\{+\infty \} ) < p_c(d)$ (in particular without any moment assumption), the convergence of some natural maximal flows towards this constant, and the continuity of this constant with regard to the distribution $G$.

Citation

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Raphaël Rossignol. Marie Théret. "Existence and continuity of the flow constant in first passage percolation." Electron. J. Probab. 23 1 - 42, 2018. https://doi.org/10.1214/18-EJP214

Information

Received: 13 September 2017; Accepted: 20 August 2018; Published: 2018
First available in Project Euclid: 26 September 2018

zbMATH: 06964793
MathSciNet: MR3862614
Digital Object Identifier: 10.1214/18-EJP214

Subjects:
Primary: 60K35
Secondary: 82B20

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