TL;DR
This paper investigates the scaled KPZ line ensembles, deriving fluctuation estimates and proving tightness, which supports the conjecture that they converge to the Airy line ensemble, advancing understanding of KPZ universality.
Contribution
It provides the first quantitative fluctuation bounds and establishes tightness for the scaled KPZ line ensembles, moving towards proving their convergence to the Airy line ensemble.
Findings
Derived quantitative local fluctuation estimates.
Proved tightness of the scaled KPZ line ensembles.
Supported the conjectural convergence to the Airy line ensemble.
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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Taxonomy
TopicsRandom Matrices and Applications · Complex Systems and Time Series Analysis · Financial Risk and Volatility Modeling