A System of PDEs for the Baik-Rains Distribution
Probability
2020-11-02 v2
Abstract
It has been discovered that the Kadomtsev-Petviashvili(KP) equation governs the distribution of the fluctuation of many random growth models, in particular, the Tracy-Widom distributions appear as special self-similar solutions of the KP equation. We prove that the anti-derivative of Baik-Rains distribution, which governs the fluctuation of the models in the KPZ universality class starting with stationary initial data, satisfies the KP equation. We start from a determinantal formula of the generating function of the KPZ equation, which satisfies the KP. Then we observe that the equation still holds in the large time limit.
Keywords
Cite
@article{arxiv.2010.09779,
title = {A System of PDEs for the Baik-Rains Distribution},
author = {Xincheng Zhang},
journal= {arXiv preprint arXiv:2010.09779},
year = {2020}
}
Comments
10 pages