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July 2015 A Hsu–Robbins–Erdős strong law in first-passage percolation
Daniel Ahlberg
Ann. Probab. 43(4): 1992-2025 (July 2015). DOI: 10.1214/14-AOP926


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. "A Hsu–Robbins–Erdős strong law in first-passage percolation." Ann. Probab. 43 (4) 1992 - 2025, July 2015.


Received: 1 June 2013; Revised: 1 January 2014; Published: July 2015
First available in Project Euclid: 3 June 2015

zbMATH: 1321.60199
MathSciNet: MR3353820
Digital Object Identifier: 10.1214/14-AOP926

Primary: 60K35
Secondary: 60F10 , 60F15

Keywords: First-passage percolation , large deviations , shape theorem

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 4 • July 2015
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