On global solutions of the random Hamilton-Jacobi equations and the KPZ problem

@article{Bakhtin2017OnGS,
  title={On global solutions of the random Hamilton-Jacobi equations and the KPZ problem},
  author={Yuri Bakhtin and Konstantin Khanin},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing tree-like structures. We believe that the KPZ universality can be explained in terms of statistics of these structures evolving in time. The paper is focussed on the setting of the random Hamilton--Jacobi equations. We formulate several conjectures concerning global… 

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