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Asymptotic expansions of some Toeplitz determinants via the topological recursion
Olivier Marchal
In this article, we study the large asymptotic expansions of Toeplitz determinants whose symbols are indicator functions of unions of arc-intervals of the unit circ…
Integrable differential systems of topological type and reconstruction by the topological recursion
Raphaël Belliard, Bertrand Eynard, Olivier Marchal
Starting from a rational Lax pair system of the form and we prove that, under certain assumptions (genus spectral c…
Loop equations from differential systems
Bertrand Eynard, Raphaël Belliard, Olivier Marchal
To any differential system where belongs to a Lie group (a fiber of a principal bundle) and is a Lie algebra valued 1-form on a Riemann surface , i…
Painlevé equations, topological type property and reconstruction by the topological recursion
Kohei Iwaki, Olivier Marchal, Axel Saenz
In this article we prove that Lax pairs associated with -dependent six Painlevé equations satisfy the topological type property proposed by Bergère, Borot and Eynard for any…