Nonexistence of Bigeodesics in Integrable Models of Last Passage Percolation

arXiv: Probability, 2018.

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Abstract:

Bi-infinite geodesics are fundamental objects of interest in planar first passage percolation. A longstanding conjecture states that under mild conditions there are almost surely no bigeodesics, however the result has not been proved in any case. For the exactly solvable model of directed last passage percolation on $mathbb{Z}^2$ with i.i...More

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