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

2019/09/15 by Márton Balázs, Ofer Busani, Timo Seppäläinen
Mathematics · #math.PR #msc:60K35 #msc:60K37

paper · pdf · doi:10.1017/fms.2020.31

published as Forum of Mathematics, Sigma, 8, E46., 2020 · 32 pages, 9 figures

arxiv created 2019/09/15 · arxiv updated 2020/11/17

Abstract

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.

Cited by

• Near-existence of bigeodesics in dynamical exponential last passage percolation