# Non-existence of bi-infinite geodesics in the exponential corner growth model

@article{Balazs2020NonexistenceOB, title={Non-existence of bi-infinite geodesics in the exponential corner growth model}, author={Marton E. Balazs and Ofer Busani and Timo Sepp{\"a}l{\"a}inen}, journal={Forum of Mathematics, Sigma}, year={2020}, volume={8} }

Abstract This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

## 23 Citations

### Geometry of geodesics through Busemann measures in directed last-passage percolation

- MathematicsJournal of the European Mathematical Society
- 2022

We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of…

### Coalescence estimates for the corner growth model with exponential weights

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- 2019

We establish estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model with i.i.d. exponential weights. There are four estimates: upper and lower bounds…

### Non-existence of bi-infinite polymer Gibbs measures.

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We show that nontrivial bi-infinite polymer Gibbs measures do not exist in typical environments in the inverse-gamma (or log-gamma) directed polymer model on the planar square lattice. The precise…

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- 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 $\mathbb{Z}^d$…

### Moderate Deviation and Exit Time Estimates for Stationary Last Passage Percolation

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- 2020

We consider planar stationary exponential Last Passage Percolation in the positive quadrant with boundary weights. For $\rho\in (0,1)$ and points $v_N=((1-\rho)^2 N,\rho^2 N)$ going to infinity along…

### Geodesics, bigeodesics, and coalescence in first passage percolation in general dimension

- Mathematics
- 2020

We consider geodesics for first passage percolation (FPP) on $\mathbb{Z}^d$ with iid passage times. As has been common in the literature, we assume that the FPP system satisfies certain basic…

### 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…

### Mixing times for the TASEP in the maximal current phase

- Mathematics
- 2021

We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a segment of size N with open boundaries. We focus on the maximal current phase, and prove that the mixing time is…

### Joint distribution of Busemann functions in the exactly solvable corner growth model

- Mathematics
- 2018

We describe the joint distribution of the Busemann functions of the corner growth model with exponential weights. The marginals of this measure are identified as the unique spatially ergodic fixed…

### FRACTAL STRUCTURE IN THE DIRECTED LANDSCAPE

- Mathematics
- 2022

. This short article surveys recent progress in investigations of fractal structure in the directed landscape, which is a putative universal scaling limit within the KPZ universality class and a…

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