The Annals of Applied Probability

A Note on Some Rates of Convergence in First-Passage Percolation

Kenneth S. Alexander

Full-text: Open access

Abstract

A variation is given of the van den Berg-Kesten inequality on the probability of disjoint occurrence of events enabling it to apply to random variables, rather than just to events, associated with various subsets of an index set. This is used to establish superadditivity of a certain family of generating functions associated with first-passage percolation. This leads to improved estimates for the rates of convergence of the expected values of certain passage times.

Article information

Source
Ann. Appl. Probab., Volume 3, Number 1 (1993), 81-90.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005508

Digital Object Identifier
doi:10.1214/aoap/1177005508

Mathematical Reviews number (MathSciNet)
MR1202516

Zentralblatt MATH identifier
0771.60090

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60E15: Inequalities; stochastic orderings

Keywords
First-passage percolation subadditivity disjoint occurrence of events

Citation

Alexander, Kenneth S. A Note on Some Rates of Convergence in First-Passage Percolation. Ann. Appl. Probab. 3 (1993), no. 1, 81--90. doi:10.1214/aoap/1177005508. https://projecteuclid.org/euclid.aoap/1177005508


Export citation