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arXiv · 1305.6260

A Hsu-Robbins-Erdős strong law in first-passage percolation

Daniel Ahlberg
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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-Erdős strong law - this strengthening is obtained without imposing a higher-order moment condition.

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Daniel Ahlberg. 2015-09-09. A Hsu-Robbins-Erdős strong law in first-passage percolation. https://doi.org/10.1214/14-aop926

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