2021/11/30 by Sean Groathouse, Groathouse, Sean, Christopher Janjigian +3 · 1 citation
Mathematics · Computer Science · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Bayesian Methods and Mixture Models
paper · pdf · doi:10.48550/arxiv.2112.00161
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 non-trivial 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 two properties of the stationary distributions which would need to be shown in order to generalize the main result to a non-solvable setting.