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1 IPHT - Institut de Physique Théorique - UMR CNRS 3681 2 CRM - Centre de Recherches Mathématiques Montréal 3 ICJ - Institut Camille Jordan Villeurbanne

Abstract : Starting from a d×d rational Lax pair system of the form ℏ∂ xΨ=LΨ and ℏ∂ tΨ=RΨ we prove that, under certain assumptions genus 0 spectral curve and additional conditions on R and L, the system satisfies the -topological type property-. A consequence is that the formal ℏ-WKB expansion of its determinantal correlators, satisfy the topological recursion. This applies in particular to all p,q minimal models reductions of the KP hierarchy, or to the six Painlevé systems.





Autor: Raphaël Belliard - Bertrand Eynard - Olivier Marchal -

Fuente: https://hal.archives-ouvertes.fr/



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