On the concentration and the convergence rate with a moment condition in first passage percolation
نویسنده
چکیده
We consider the first passage percolation model on the Zd 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) and Talagrand (1995) investigated the concentration of a0,n from its mean using different methods. With this concentration and the exponential tail assumption, Alexander gave an estimate for the convergence rate for Ea0,n. In this paper, focusing on a moment condition, we reinvestigate the concentration and the convergence rate for a0,n using a special martingale structure.
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