Subgaussian rates of convergence of means in directed first passage percolation

Abstract

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, $E{a}_{0n}-n\mu =O(n^{1/2}(\log \log n)/\log n)$.

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

References in corpus (1)

• Second class particles and cube root asymptotics for Hammersley's process

Cited by in corpus (2)

• Subgaussian concentration and rates of convergence in directed polymers
• Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian