Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data

2025/09/23 by Pantelis Tassopoulos, Tassopoulos, Pantelis, Sourav Sarkar +1
Computer Science · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2509.19415

openalex publication_date 2025/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the spatial increments of the KPZ fixed point starting from arbitrary initial data, exhibit strong quantitative comparison against rate two Brownian motion on compacts. The above estimates are uniform in the initial data supported in some compact set. As applications, we obtain a one-sided large deviation inequality for spatial increments of the KPZ fixed point and show that the Wiener density of the centred KPZ fixed point started from arbitrary initial data has finite entropy.

Citations

• Radon-Nikodym derivative of inhomogeneous Brownian last passage percolation
• Applications of optimal transport to Dyson Brownian Motions and beyond
• Characterization of the directed landscape from the KPZ fixed point
• Wiener densities for the Airy line ensemble
• Sharp upper tail behavior of line ensembles via the tangent method
• Random metric geometries on the plane and Kardar-Parisi-Zhang universality
• Characterization of Brownian Gibbsian line ensembles
• Brownian Aspects of the KPZ Fixed Point
• Arctic Boundaries of the Ice Model on Three-Bundle Domains
• The directed landscape
• The two-time distribution in geometric last-passage percolation
• A patchwork quilt sewn from Brownian fabric: regularity of polymer weight profiles in Brownian last passage percolation
• Kardar-Parisi-Zhang Universality
• On the local fluctuations of last-passage percolation models
• Brownian Gibbs property for Airy line ensembles
• Local Gaussian fluctuations in the Airy and discrete PNG processes
• Scale Invariance of the PNG Droplet and the Airy Process
• On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations

Related

• Brownian Aspects of the KPZ Fixed Point
• Spatial decorrelation of KPZ from narrow wedge
• Ergodicity of the KPZ Fixed Point
• Brownian regularity for the KPZ line ensemble
• Long and short time laws of iterated logarithms for the KPZ fixed point