# Absence of backward infinite paths for first-passage percolation in arbitrary dimension

@article{Brito2020AbsenceOB, title={Absence of backward infinite paths for first-passage percolation in arbitrary dimension}, author={Gerandy Brito and Michael Damron and Jack Hanson}, journal={arXiv: Probability}, year={2020} }

In first-passage percolation (FPP), one places nonnegative random variables (weights) $(t_e)$ on the edges of a graph and studies the induced weighted graph metric. We consider FPP on $\mathbb{Z}^d$ for $d \geq 2$ and analyze the geometric properties of geodesics, which are optimizing paths for the metric. Specifically, we address the question of existence of bigeodesics, which are doubly-infinite paths whose subpaths are geodesics. It is a famous conjecture originating from a question of…

## 4 Citations

Empirical distributions, geodesic lengths, and a variational formula in first-passage percolation.

- Mathematics
- 2020

This article resolves, in a dense set of cases, several open problems concerning geodesics in i.i.d. first-passage percolation on $\mathbb{Z}^d$. Our primary interest is in the empirical measures of…

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

- Mathematics
- 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…

Random nearest neighbor graphs: the translation invariant case

- Mathematics
- 2020

If $(\omega(e))$ is a family of random variables (weights) assigned to the edges of $\mathbb{Z}^d$, the nearest neighbor graph is the directed graph induced by all edges $\langle x,y \rangle$ such…

Existence and Coexistence in First-Passage Percolation

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- 2020

We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of geodesics in…

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