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

Ahlberg, Daniel. ^[1]
1. [1] Instituto Nacional de Matemática Pura e Aplicada
  
  Instituto Nacional de Matemática Pura e Aplicada
  
  Brasil
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 4, 2015, págs. 1992-2025
Idioma: inglés
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Resumen
- 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.