No abstract

International audienceStarting from a d × d rational Lax pair system of the form ∂ x Ψ = LΨ and ∂ t Ψ = 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-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