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

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  • Zhang, Yu

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.

Suggested Citation

  • Zhang, Yu, 2010. "On the concentration and the convergence rate with a moment condition in first passage percolation," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1317-1341, July.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:7:p:1317-1341
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    1. Zhang, Yu, 1995. "Supercritical behaviors in first-passage percolation," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 251-266, October.
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    Cited by:

    1. Damron, Michael & Kubota, Naoki, 2016. "Rate of convergence in first-passage percolation under low moments," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3065-3076.

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