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The geometry of coalescing random walks, the Brownian web distance and KPZ universality

Bálint Vető & Bálint Virág

Annals of Probability2026https://doi.org/10.1214/25-aop1772preprint
ABDC A*
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0.50

Abstract

Coalescing simple random walks in the plane form an infinite tree. A natural directed distance on this tree is given by the number of jumps between branches when one is only allowed to move in one direction. The Brownian web distance is the scale-invariant limit of this directed metric. It is integer-valued and has scaling exponents 0:1:2 as compared to 1:2:3 in the KPZ world. However, we show that the shear limit of the Brownian web distance is still given by the Airy process. We conjecture that our limit theorem can be extended to the full directed landscape.

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https://doi.org/https://doi.org/10.1214/25-aop1772

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@article{bálint2026,
  title        = {{The geometry of coalescing random walks, the Brownian web distance and KPZ universality}},
  author       = {Bálint Vető & Bálint Virág},
  journal      = {Annals of Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-aop1772},
}

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The geometry of coalescing random walks, the Brownian web distance and KPZ universality

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F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
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R · text relevance †0.50 × 0.4 = 0.20

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