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Mathematics > Probability

arXiv:1812.00309 (math)
[Submitted on 2 Dec 2018 (v1), last revised 12 Oct 2022 (this version, v7)]

Title:The directed landscape

Authors:Duncan Dauvergne, Janosch Ortmann, Balint Virag
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Abstract:The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and characterize it in terms of the Airy line ensemble. We also show that last passage geodesics converge to random functions with Holder-2/3- continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class, the directed landscape.
Comments: 78 pages, 6 figures
Subjects: Probability (math.PR); Mathematical Physics (math-ph)
MSC classes: 60K35, 60B20
Cite as: arXiv:1812.00309 [math.PR]
  (or arXiv:1812.00309v7 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.00309
Journal reference: Acta Mathematica, 229, 201-285, 2022
Related DOI: https://doi.org/10.4310/ACTA.2022.v229.n2.a1

Submission history

From: Duncan Dauvergne [view email]
[v1] Sun, 2 Dec 2018 02:41:51 UTC (51 KB)
[v2] Sat, 18 May 2019 14:29:37 UTC (229 KB)
[v3] Sat, 22 Jun 2019 16:03:16 UTC (229 KB)
[v4] Tue, 16 Jun 2020 20:12:38 UTC (238 KB)
[v5] Wed, 9 Jun 2021 15:06:00 UTC (242 KB)
[v6] Mon, 19 Jul 2021 16:24:51 UTC (242 KB)
[v7] Wed, 12 Oct 2022 15:01:07 UTC (242 KB)
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