Georgiou, Nicos, Rassoul-Agha, Firas and Seppäläinen, Timo (2016) Geodesics and the competition interface for the corner growth model. Probability Theory and Related Fields, 169 (1-2). pp. 223-255. ISSN 0178-8051
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Abstract
We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface.
Item Type: | Article |
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Keywords: | Busemann function, coalescence, cocycle, competition interface, directed percolation, geodesic, last-passage percolation. |
Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
Research Centres and Groups: | Probability and Statistics Research Group |
Subjects: | Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics |
Depositing User: | Nicos Georgiou |
Date Deposited: | 28 Nov 2016 07:20 |
Last Modified: | 12 Sep 2018 16:05 |
URI: | http://srodev.sussex.ac.uk/id/eprint/65686 |
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