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Fredholm-Determinant Tau Functions of the q-Painleve III3 Equation

A Riemann-Hilbert construction on a circle whose Fredholm determinant is the isomonodromic tau function of the q-Painleve equation of type A7^(1)'. The determinant obeys bilinear relations equivalent to the q-Painleve equation, expands as a factorized Fourier series of q-deformed conformal blocks and 5d N=1 SU(2) Nekrasov partition functions, and its connection problem gives the tau function's global asymptotics.

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Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection

Reformulates the linear q-difference system associated with the q-Painleve equation of type A7^(1)' (a discrete analogue of Painleve III) as a Riemann-Hilbert problem on a circle, and builds a Fredho…