3 papers
math.PR2026
Classification of the eternal solutions and multiple coalescing shocks in the KPZ fixed point
Sudeshna Bhattacharjee, Ofer Busani, Evan Sorensen
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…
math.PR2025
Jointly invariant measures for the Kardar-Parisi-Zhang Equation
Sean Groathouse, Firas Rassoul-Agha, Timo Seppäläinen +1
We give an explicit description of the jointly invariant measures for the KPZ equation. These are couplings of Brownian motions with drift, and can be extended to a process defined…
math.PR2024
Scaling limit of multi-type invariant measures via the directed landscape
Ofer Busani, Timo Seppäläinen, Evan Sorensen
This paper studies the large scale limits of multi-type invariant distributions and Busemann functions of planar stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class. We…