Polynuclear growth and the Toda lattice
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914914238464000 |
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| author | Matetski, Konstantin Quastel, Jeremy Remenik, Daniel |
| author_facet | Matetski, Konstantin Quastel, Jeremy Remenik, Daniel |
| contents | It is shown that the polynuclear growth model is a completely integrable Markov process in the sense that its transition probabilities are given by Fredholm determinants of kernels produced by a scattering transform based on the invariant measures modulo the absolute height, continuous time simple random walks. From the linear evolution of the kernels, it is shown that the $n$-point distributions are determinants of $n\times n$ matrices evolving according to the two dimensional non-Abelian Toda lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02643 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Polynuclear growth and the Toda lattice Matetski, Konstantin Quastel, Jeremy Remenik, Daniel Probability Mathematical Physics Exactly Solvable and Integrable Systems It is shown that the polynuclear growth model is a completely integrable Markov process in the sense that its transition probabilities are given by Fredholm determinants of kernels produced by a scattering transform based on the invariant measures modulo the absolute height, continuous time simple random walks. From the linear evolution of the kernels, it is shown that the $n$-point distributions are determinants of $n\times n$ matrices evolving according to the two dimensional non-Abelian Toda lattice. |
| title | Polynuclear growth and the Toda lattice |
| topic | Probability Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2209.02643 |