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A phase transition for competition interfaces

Abstract:

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle $\theta$ of the cone: for $\theta\geq180^{\circ}$, the direction is deterministic, while for $\theta<180^{\circ}$, it is random, and its distribution can be given explicitly in certain ca...

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Publication status:
Published

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Publisher copy:
10.1214/08-AAP542

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
Journal:
Annals of Applied Probability More from this journal
Volume:
19
Issue:
1
Pages:
281-317
Publication date:
2007-01-15
DOI:
EISSN:
1050-5164
ISSN:
1050-5164
Language:
English
Keywords:
Pubs id:
pubs:97442
UUID:
uuid:f6322710-98a9-4a54-be9c-e2c3f038e597
Local pid:
pubs:97442
Source identifiers:
97442
Deposit date:
2012-12-19

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