A Hsu-Robbins-Erd\H{o}s strong law in first-passage percolation
Abstract
Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these studies provides a precise relation between the existence of moments of polynomial order and the decay of probability tails. Such a relation is derived in this paper, and is used to strengthen the conclusion of the shape theorem. In contrast to its one-dimensional counterpart - the Hsu-Robbins-Erd\H{o}s strong law - this strengthening is obtained without imposing a higher-order moment condition.
Keywords
Cite
@article{arxiv.1305.6260,
title = {A Hsu-Robbins-Erd\H{o}s strong law in first-passage percolation},
author = {Daniel Ahlberg},
journal= {arXiv preprint arXiv:1305.6260},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.1214/14-AOP926 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)