Vető, Bálint and Virág, Bálint (2026) The geometry of coalescing random walks, the Brownian web distance and KPZ universality. ANNALS OF PROBABILITY. ISSN 0091-1798 (In Press)
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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 integervalued 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.
| Item Type: | Article |
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| Uncontrolled Keywords: | coalescing random walks, Brownian web, random geometry, KPZ universality |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 06 Feb 2026 08:37 |
| Last Modified: | 06 Feb 2026 08:37 |
| URI: | https://real.mtak.hu/id/eprint/233464 |
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