定向景观

IF 4.9 1区数学 Q1 MATHEMATICS

Acta Mathematica Pub Date : 2018-12-02 DOI:10.4310/acta.2022.v229.n2.a1

Duncan Dauvergne, Janosch Ortmann, B'alint Vir'ag

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引用次数: 116

摘要

最后一次渗流的推测极限是一个尺度不变的、独立的、相对于度量组成的平稳增量过程。我们为布朗最后一次渗流证明了这一点。我们构造了艾里片，并根据艾里线系综对其进行了表征。我们还证明了最后一段测地线收敛于Holder-$2/3^-$连续路径的随机函数。本作品完成了张普适性类中心对象的建构，即指向性景观。

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The directed landscape

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.

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