Upper large deviations for the maximal flow in first-passage percolation

Marie Théret

Stochastic Processes and their Applications, 2007, vol. 117, issue 9, 1208-1233

Abstract: We consider the standard first-passage percolation in for d>=2 and we denote by [phi]nd-1,h(n) the maximal flow through the cylinder ]0,n]d-1x]0,h(n)] from its bottom to its top. Kesten proved a law of large numbers for the maximal flow in dimension 3: under some assumptions, [phi]nd-1,h(n)/nd-1 converges towards a constant [nu]. We look now at the probability that [phi]nd-1,h(n)/nd-1 is greater than [nu]+[epsilon] for some [epsilon]>0, and we show under some assumptions that this probability decays exponentially fast with the volume nd-1h(n) of the cylinder. Moreover, we prove a large deviation principle for the sequence .

Keywords: First-passage; percolation; Large; deviations; Maximal; flow; Max-flow; min-cut (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00195-5
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:117:y:2007:i:9:p:1208-1233

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().