On the concentration and the convergence rate with a moment condition in first passage percolation
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.
Year of publication: |
2010
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Authors: | Zhang, Yu |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 120.2010, 7, p. 1317-1341
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Publisher: |
Elsevier |
Keywords: | First passage percolation Concentration Convergence rate A moment condition |
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