Subgaussian rates of convergence of means in directed first passage percolation

Details Subgaussian rates of convergence of means in directed first passage percolation Subgaussian rates of convergence of means in directed first passage percolation

2011-01-07

arxiv.org/abs/1101.1549v3

Mathematics

Probability

Miscellaneous small errors corrected, particularly in the proof of Lemma 3.1; new definition of the augmented climbing skeleto

Scientific paper

We consider directed first passage percolation on the integer lattice, with
time constant $\mu$ and passage time $a_{0n}$ from the origin to $(n,0,...,0)$.
It is shown that under certain conditions on the passage time distribution,
$Ea_{0n} - n\mu = O(n^{1/2}(\log\log n)/\log n)$.

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