Brownian regularity for the KPZ line ensemble

Abstract

This paper seeks a quantitative comparison between the curves in the KPZ line ensemble [CH16] and a standard Brownian bridge under the $t^{1/3}$ vertical and $t^{2/3}$ horizontal scaling. The estimate we obtained is parallel to the one established in [Ham1], where the Airy line ensemble was studied. Our main tool is the soft Brownian Gibbs property enjoyed by the KPZ line ensemble. In view of the Gibbs property, the KPZ line ensemble differs from the Airy line ensemble mainly due to the intersecting nature of its curves, which results in the main technical difficulty in this paper. We develop a resampling framework, the soft jump ensemble, to tackle this difficulty. Our method is highly inspired by the jump ensemble technique developed in [Ham1].

References in corpus (6)

• The one-dimensional KPZ equation and its universality class
• The directed landscape
• Exponents governing the rarity of disjoint polymers in Brownian last passage percolation
• Bulk properties of the Airy line ensemble
• The heat and the landscape I
• Tightness of discrete Gibbsian line ensembles with exponential interaction Hamiltonians