Classification of the eternal solutions and multiple coalescing shocks in the KPZ fixed point
Probability
2026-05-26 v1 Mathematical Physics
math.MP
Abstract
We give a complete classification of the eternal solutions for the KPZ fixed point. Each of these is a (possibly infinite) patching together of the known eternal solutions, called Busemann functions. The resulting evolution of the KPZ fixed point exhibits a shock at each of the boundaries between the different Busemann functions. Moving forward in time, the shocks coalesce, while moving backwards in time, additional shocks can form. We describe several geometric properties of this tree of shocks.
Cite
@article{arxiv.2605.26048,
title = {Classification of the eternal solutions and multiple coalescing shocks in the KPZ fixed point},
author = {Sudeshna Bhattacharjee and Ofer Busani and Evan Sorensen},
journal= {arXiv preprint arXiv:2605.26048},
year = {2026}
}
Comments
29 pages, 2 figures