Geodesics and the competition interface 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/s00440-016-0734-0
• 发表日期: 2017
• 页码: 223-255
• 关键词: 1st passage percolation; 2-dimensional 1st-passage percolation; 2nd class particle; burgers-equation; lagrangian systems; infinite geodesics; busemann functions; rarefaction fan; ./gi/1 queue; fixed-points

摘要

We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. In Georgiou et al. (Probab Theory Relat Fields, 2016, doi:10.1007/s00440-016-0729-x) we constructed stationary cocycles and Busemann functions for this model. Using these objects, we prove new results on the competition interface, on existence, uniqueness, and coalescence of directional semi-infinite geodesics, and on nonexistence of doubly infinite geodesics.