CPL - Chalmers Publication Library
| Utbildning | Forskning | Styrkeområden | Om Chalmers | In English In English Ej inloggad.

Asymptotics of First-Passage Percolation on One-Dimensional Graphs

Daniel Ahlberg (Institutionen för matematiska vetenskaper, matematisk statistik)
Advances in Applied Probability (0001-8678). Vol. 47 (2015), 1, p. 182-209.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: First-passage percolation, renewal theory, classical limit theorem

Denna post skapades 2015-06-04.
CPL Pubid: 218037


Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)



Chalmers infrastruktur