On the Crystal Limit of the q-Difference Sixth Painlevé Equation

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.