论文标题
Lipschitz的约束最长的路径增加
Longest increasing paths with Lipschitz constraints
论文作者
论文摘要
Hammersley问题要求通过泊松点过程中单调路径中的最大点数。它完全可以解决且众所周知，属于KPZ通用类别，具有多维数据的缩放，以进行波动。在此，我们介绍和分析了一种变体，其中我们在路径上施加了Lipschitz条件。多亏了与经典的Hammersley问题的结合，我们观察到该变体也可以解决。它使我们能够衍生渐近学。事实证明，立方根缩放仅适用于Lipschitz常数的某些选择。
The Hammersley problem asks for the maximal number of points in a monotonous path through a Poisson point process. It is exactly solvable and notoriously known to belong to the KPZ universality class, with a cube-root scaling for the fluctuations.Here we introduce and analyze a variant in which we impose a Lipschitz condition on paths. Thanks to a coupling with the classical Hammersley problem we observe that this variant is also exactly solvable. It allows us to derive first and second orders asymptotics. It turns out that the cube-root scaling only holds for certain choices of the Lipschitz constants.
