• Corpus ID: 244773243

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

@inproceedings{Groathouse2021NonexistenceON,
  title={Non-existence of non-trivial bi-infinite geodesics in Geometric Last Passage Percolation},
  author={Sean Groathouse and Christopher Janjigian and Firas Rassoul-Agha},
  year={2021}
}
— 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… 

Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation

TLDR
New probabilistic arguments are introduced to derive optimal-order central moment bounds in planar directed last-passage percolation in i.i.d. exponential weights for both zero and near-stationary boundary conditions.

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