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**Harvard**

Ahlberg, D. (2015) *Asymptotics of First-Passage Percolation on One-Dimensional Graphs*.

** BibTeX **

@article{

Ahlberg2015,

author={Ahlberg, Daniel},

title={Asymptotics of First-Passage Percolation on One-Dimensional Graphs},

journal={Advances in Applied Probability},

issn={0001-8678},

volume={47},

issue={1},

pages={182-209},

abstract={In this paper we consider first-passage percolation on certain one-dimensional periodic graphs, such as the Z x {0, 1, ..., K - 1}(d-1) nearest neighbour graph for d, K >= 1. We expose a regenerative structure within the first-passage process, and use this structure to show that both length and weight of minimal-weight paths present a typical one-dimensional asymptotic behaviour. Apart from a strong law of large numbers, we derive a central limit theorem, a law of the iterated logarithm, and a Donsker theorem for these quantities. In addition, we prove that the mean and variance of the length and weight of minimizing paths are monotone in the distance between their end-points, and further show how the regenerative idea can be used to couple two first-passage processes to eventually coincide. Using this coupling we derive a 0-1 law.},

year={2015},

keywords={First-passage percolation, renewal theory, classical limit theorem},

}

** RefWorks **

RT Journal Article

SR Print

ID 218037

A1 Ahlberg, Daniel

T1 Asymptotics of First-Passage Percolation on One-Dimensional Graphs

YR 2015

JF Advances in Applied Probability

SN 0001-8678

VO 47

IS 1

SP 182

OP 209

AB In this paper we consider first-passage percolation on certain one-dimensional periodic graphs, such as the Z x {0, 1, ..., K - 1}(d-1) nearest neighbour graph for d, K >= 1. We expose a regenerative structure within the first-passage process, and use this structure to show that both length and weight of minimal-weight paths present a typical one-dimensional asymptotic behaviour. Apart from a strong law of large numbers, we derive a central limit theorem, a law of the iterated logarithm, and a Donsker theorem for these quantities. In addition, we prove that the mean and variance of the length and weight of minimizing paths are monotone in the distance between their end-points, and further show how the regenerative idea can be used to couple two first-passage processes to eventually coincide. Using this coupling we derive a 0-1 law.

LA eng

OL 30