Electronic Communications in Probability

Multiple geodesics with the same direction

David Coupier

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Abstract

The directed last-passage percolation (LPP) model with independent exponential times is considered. We complete the study of asymptotic directions of infinite geodesics, started by Ferrari and Pimentel [5]. In particular, using a recent result of [3] and a local modification argument, we prove there is no (random) direction with more than two geodesics with probability 1.

Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 46, 517-527.

Dates
Accepted: 26 September 2011
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465262002

Digital Object Identifier
doi:10.1214/ECP.v16-1656

Mathematical Reviews number (MathSciNet)
MR2836758

Zentralblatt MATH identifier
1244.60093

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

Keywords
geodesic last-passage percolation topological end random tree

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Coupier, David. Multiple geodesics with the same direction. Electron. Commun. Probab. 16 (2011), paper no. 46, 517--527. doi:10.1214/ECP.v16-1656. https://projecteuclid.org/euclid.ecp/1465262002


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