Journal Articles Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Year : 2022

Longest increasing paths with Lipschitz constraints

Abstract

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.
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Dates and versions

hal-02437174 , version 1 (13-01-2020)
hal-02437174 , version 2 (16-12-2021)

Identifiers

Cite

Anne-Laure Basdevant, Lucas Gerin. Longest increasing paths with Lipschitz constraints. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022, 58 (3), ⟨10.1214/21-AIHP1220⟩. ⟨hal-02437174v2⟩
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