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Geodesics and the competition interface for the corner growth model

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posted on 2023-06-09, 04:13 authored by Nicos GeorgiouNicos Georgiou, Firas Rassoul-Agha, Timo Seppäläinen
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Probability Theory and Related Fields

ISSN

0178-8051

Publisher

Springer Verlag

Issue

1-2

Volume

169

Page range

223-255

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-11-28

First Open Access (FOA) Date

2017-08-11

First Compliant Deposit (FCD) Date

2016-11-27

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