Convergence of the KPZ line ensemble

2021/06/15 by Xuan Wu, Wu, Xuan · 1 citation
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Random Matrices and Applications #math.PR

paper · pdf · doi:10.48550/arxiv.2106.08051

openalex publication_date 2021/06/15 · arxiv created 2022/01/25 · arxiv updated 2022/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the KPZ line ensembles under the KPZ scaling. Based on their Gibbs property, we derive quantitative local fluctuation estimates for the scaled KPZ line ensembles. This allows us to show that the family of scaled KPZ line ensembles is tight. Together with the recent progress in [QS20], [Vir], and [DM], the tightness result yields the conjectural convergence of the scaled KPZ line ensembles to the Airy line ensemble.

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• van den Berg-Kesten--type correlation inequalities for disjoint polymers in the KPZ universality class

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