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

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dc.creatorZhang, Yu
dc.date2008-08-22
dc.date.accessioned2026-07-07T09:57:54Z
dc.date.available2026-07-07T09:57:54Z
dc.descriptionWe consider the first passage percolation model on the ${\bf Z}^d$ lattice. In this model, we assign independently to each edge $e$ a non-negative passage time $t(e)$ with a common distribution $F$. Let $a_{0,n}$ be the passage time from the origin to $(n,0,..., 0)$. Under the exponential tail assumption, Kesten (1993) and Talagrand (1995) investigated the concentration of $a_{0,n}$ from its mean using different methods. With this concentration and the exponential tail assumption, Alexander gave an estimate for the convergence rate for ${\bf E} a_{0,n}$. In this paper, focusing on a moment condition, we reinvestigate the concentration and the convergence rate for $a_{0,n}$ using a special martingale structure.
dc.description27 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0808.3021
dc.identifierhttp://arxiv.org/abs/0808.3021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167520
dc.subjectProbability
dc.subject60K35
dc.titleOn the concentration and the convergence rate with a moment condition in first passage percolation
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