2021
DOI: 10.48550/arxiv.2112.00161
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Non-existence of non-trivial bi-infinite geodesics in Geometric Last Passage Percolation

Abstract: We show non-existence of non-trivial bi-infinite geodesics in the solvable last-passage percolation model with i.i.d. geometric weights. This gives the first example of a model with discrete weights where non-existence of nontrivial bi-infinite geodesics has been proven. Our proofs rely on the structure of the increment-stationary versions of the model, following the approach recently introduced by Balázs, Busani, and Seppäläinen. Most of our results work for a general weights distribution and we identify the … Show more

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“…Our approach should in principle be fully implementable in any of these settings. As supporting evidence in this regard, the recent preprint [64] derives among other results essentially the analogues of our inputs from [49,50] for the geometric LPP. A similar development is currently underway for the four basic integrable lattice polymers as well [51].…”
Section: ´1supporting
confidence: 66%
“…Our approach should in principle be fully implementable in any of these settings. As supporting evidence in this regard, the recent preprint [64] derives among other results essentially the analogues of our inputs from [49,50] for the geometric LPP. A similar development is currently underway for the four basic integrable lattice polymers as well [51].…”
Section: ´1supporting
confidence: 66%