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We show non-existence of non-trivial bi-infinite geodesics in the solvablelast-passage percolation model with i.i.d. geometric weights. This gives thefirst example of a model with discrete weights where non-existence ofnon-trivial bi-infinite geodesics has been proven. Our proofs rely on thestructure of the increment-stationary versions of the model, following theapproach recently introduced by Bal\'azs, Busani, and Sepp\"al\"ainen. Most ofour results work for a general weights distribution and we identify the twoproperties of the stationary distributions which would need to be shown inorder to generalize the main result to a non-solvable setting.

Non-existence of non-trivial bi-infinite geodesics in Geometric Last Passage Percolation