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The metric removability of interfaces in the directed landscape

Manan Bhatia

Annals of Applied Probability2026https://doi.org/10.1214/25-aap2256article
ABDC A
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0.50

Abstract

The directed landscape is a prominent model of random geometry which is believed to be the universal scaling limit of all planar random geometries in the Kardar–Parisi–Zhang universality class. It comes equipped with a few different natural simple curves associated to it, such as geodesics and interfaces. Given such a curve, one might wonder whether the geometry of this curve determines the entire landscape, or if in fact, there is nontrivial extra information actually present “on” the curve. In this paper, we show that the former is true for an interface in the directed landscape, while the latter is true for a geodesic instead. Further, as is used in the proof of the first assertion above, we precisely identify the correct Hausdorff dimension of the set of times where any geodesic intersects an interface—we show that this set a.s. has dimension zero.

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https://doi.org/https://doi.org/10.1214/25-aap2256

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@article{manan2026,
  title        = {{The metric removability of interfaces in the directed landscape}},
  author       = {Manan Bhatia},
  journal      = {Annals of Applied Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-aap2256},
}

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The metric removability of interfaces in the directed landscape

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