The Annals of Probability
- Ann. Probab.
- Volume 43, Number 4 (2015), 1992-2025.
A Hsu–Robbins–Erdős strong law in first-passage percolation
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–Erdős strong law—this strengthening is obtained without imposing a higher-order moment condition.
Ann. Probab., Volume 43, Number 4 (2015), 1992-2025.
Received: June 2013
Revised: January 2014
First available in Project Euclid: 3 June 2015
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Ahlberg, Daniel. A Hsu–Robbins–Erdős strong law in first-passage percolation. Ann. Probab. 43 (2015), no. 4, 1992--2025. doi:10.1214/14-AOP926. https://projecteuclid.org/euclid.aop/1433341325