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Polynuclear growth and the Toda lattice

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arxiv 2209.02643 v2 pith:2EPRAOSX submitted 2022-09-06 math.PR math-phmath.MPnlin.SI

Konstantin Matetski , Jeremy Quastel , Daniel Remenik This is my paper · ORCID
classification math.PRmath-phmath.MPnlin.SI
keywords determinantsgrowthkernelslatticepolynucleartodaabsoluteaccording
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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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