# A System of PDEs for the Baik-Rains Distribution

@article{Zhang2020ASO, title={A System of PDEs for the Baik-Rains Distribution}, author={Xincheng Zhang}, journal={arXiv: Probability}, year={2020} }

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…

## One Citation

### Integrable fluctuations in the KPZ universality class

- Mathematics
- 2022

A BSTRACT . The KPZ ﬁxed point is a scaling invariant Markov process which arises as the universal scaling limit of a broad class of models of random interface growth in one dimension, the…

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