• Corpus ID: 245123952

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… 
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