Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data
Probability
2026-05-01 v4
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.
Keywords
Cite
@article{arxiv.2509.19415,
title = {Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data},
author = {Pantelis Tassopoulos and Sourav Sarkar},
journal= {arXiv preprint arXiv:2509.19415},
year = {2026}
}
Comments
This version significantly improves the form of quantitative Brownian regularity, streamlines the proof, fixes some typos and changes some figures