Stationary cocycles and Busemann functions for the corner growth model

Georgiou, Nicos, Rassoul-Agha, Firas and Seppäläinen, Timo (2016) Stationary cocycles and Busemann functions for the corner growth model. Probability Theory and Related Fields. 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
Keywords: Busemann function, cocycle, competition interface, directed percolation, geodesic, last-passage percolation, percolation cone, queueing fixed point, variational formula.
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 07:16
Last Modified: 05 Aug 2017 20:14
URI: http://sro.sussex.ac.uk/id/eprint/65687

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