Subgaussian rates of convergence of means in directed first passage percolation

2011/01/07 by Kenneth S. Alexander, Alexander, Kenneth S.
Mathematics · #60K35 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.1101.1549

Miscellaneous small errors corrected, particularly in the proof of Lemma 3.1; new definition of the augmented climbing skeleton; proof of Theorem 2.1 added. 17 pages

arxiv created 2011/05/18 · arxiv updated 2011/05/19

Abstract

We consider directed first passage percolation on the integer lattice, with time constant μ 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 - nμ= O(n^1/2(loglog n)/log n).

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