Nonexistence of nontrivial biinfinite geodesics in Geometric Last Passage Percolation
Abstract
We show nonexistence of nontrivial biinfinite geodesics in the solvable lastpassage percolation model with i.i.d. geometric weights. This gives the first example of a model with discrete weights where nonexistence of nontrivial biinfinite geodesics has been proven. Our proofs rely on the structure of the incrementstationary 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 two properties of the stationary distributions which would need to be shown in order to generalize the main result to a nonsolvable setting.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2112.00161
 Bibcode:
 2021arXiv211200161G
 Keywords:

 Mathematics  Probability;
 60K35;
 60K37
 EPrint:
 37 pages, 4 figures