On the local fluctuations of last-passage percolation models

2013/11/06 by Eric Cator, Cator, Eric, Leandro P. R. Pimentel +2 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1311.1349

14 pages

arxiv created 2013/11/06 · openalex publication_date 2013/11/06 · arxiv updated 2013/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the fact that the Airy process describes the limiting fluctuations of the Hammersley last-passage percolation model, we prove that it behaves locally like a Brownian motion. Our method is quite straightforward, and it is based on a certain monotonicity and good control over the equilibrium measures of the Hammersley model (local comparison).

Cited by

• Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data
• Sprinkled Decoupling for Hammersley's Process
• Near-existence of bigeodesics in dynamical exponential last passage percolation

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