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arXiv · 2209.02643

Polynuclear growth and the Toda lattice

Konstantin Matetski·Jeremy Quastel·Daniel Remenik
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Abstract

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.

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Konstantin Matetski, Jeremy Quastel, Daniel Remenik. 2022-09-06. Polynuclear growth and the Toda lattice. https://arxiv.org/abs/2209.02643

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