Non-existence of bi-infinite geodesics in the exponential corner growth model

Marton Balazs, Ofer Busani*, Timo Seppäläinen

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review


This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.
Original languageEnglish
Pages (from-to)E46
Number of pages32
JournalForum of Mathematics, Sigma
Publication statusPublished - 16 Nov 2020


  • bi-infinite, corner growth model, directed percolation, geodesic, random growth model, last-passage percolation, queues


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