Stationary cocycles and Busemann functions for the corner growth model

• 成果类型: Article
• 署名作者: Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo
• 署名单位: University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0729-x
• 发表日期: 2017
• 页码: 177-222
• 关键词: 1st passage percolation; 2-dimensional 1st-passage percolation; 2nd class particles; burgers-equation; competition interfaces; boundary-conditions; lagrangian systems; random environment; directed polymers; random potentials

摘要

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, outside of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as boundary 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.