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arXiv · 2408.07963

On the crystal limit of the q-difference sixth Painlevé equation

Nalini Joshi·Pieter Roffelsen
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Abstract

We consider the Riemann-Hilbert correspondence associated with the $q$-difference sixth Painlevé equation in the crystal limit, i.e. $q\rightarrow 0$, and show two main results. First, the limit of this generically highly transcendental mapping is shown to exist. Second, we show that the limiting map is bi-rational and describe it explicitly.

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Nalini Joshi, Pieter Roffelsen. 2025-01-02. On the crystal limit of the q-difference sixth Painlevé equation. https://arxiv.org/abs/2408.07963

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