# Infinite geodesics, competition interfaces and the second class particle in the scaling limit

@inproceedings{Rahman2021InfiniteGC, title={Infinite geodesics, competition interfaces and the second class particle in the scaling limit}, author={Mustazee Rahman and B{\'a}lint Vir{\'a}g}, year={2021} }

We establish fundamental properties of infinite geodesics and competition interfaces in the directed landscape. We construct infinite geodesics in the directed landscape, establish their uniqueness and coalescence, and define Busemann functions. We show the second class particle in tasep converges under KPZ scaling to a competition interface. Under suitable conditions we show the competition interface has an asymptotic direction, analogous to the speed of a second class particle in tasep, and…

## 2 Citations

Diffusive scaling limit of the Busemann process in Last Passage Percolation

- Mathematics
- 2021

In exponential last passage percolation, we consider the rescaled Busemann process x 7→ N−1/2B 0,[xN ]e1 (x ∈ R), as a process parametrized by the scaled density ρ = 1/2+μ4N −1/2, and taking values…

The stationary horizon and semi-infinite geodesics in the directed landscape

- Mathematics
- 2022

. The stationary horizon is a stochastic process consisting of coupled Brownian motions, indexed by their real-valued drifts. It was recently constructed by the ﬁrst author as the scaling limit of…

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