On the concentration and the convergence rate with a moment condition in first passage percolation

Yu Zhang

Stochastic Processes and their Applications, 2010, vol. 120, issue 7, 1317-1341

Abstract: We consider the first passage percolation model on the lattice. In this model, we assign independently to each edge e a non-negative passage time t(e) with a common distribution F. Let a0,n be the passage time from the origin to (n,0,...,0). Under the exponential tail assumption, Kesten (1993) [9] and Talagrand (1995) [12] investigated the concentration of a0,n from its mean using different methods. With this concentration and the exponential tail assumption, Alexander (1993) [1] gave an estimate for the convergence rate for . In this paper, focusing on a moment condition, we reinvestigate the concentration and the convergence rate for a0,n using a special martingale structure.

Keywords: First; passage; percolation; Concentration; Convergence; rate; A; moment; condition (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00048-7
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:120:y:2010:i:7:p:1317-1341

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 ().