Explicit closed algebraic formulas for Orlov-Scherbin $n$-point functions

Abstract

We derive a new explicit formula in terms of sums over graphs for the $n$-point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev-Petviashvili tau functions of hypergeometric type (also known as Orlov-Scherbin partition functions). Notably, we use the change of variables suggested by the associated spectral curve, and our formula turns out to be a polynomial expression in a certain small set of formal functions defined on the spectral curve.

arXiv comment35 pages; minor changes

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Cited by in corpus (17)

• Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
• On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator
• A simple formula for the $x$-$y$ symplectic transformation in topological recursion
• Laplace transform of the $x-y$ symplectic transformation formula in Topological Recursion
• KP integrability through the $x-y$ swap relation
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• Degenerate and irregular topological recursion
• Log topological recursion through the prism of $x-y$ swap
• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III
• Symplectic duality for topological recursion
• Topological recursion, symplectic duality, and generalized fully simple maps
• Symplectic (Non-)Invariance of the Free Energy in Topological Recursion
• Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected $(n,m)$-Point Functions, and Double Hurwitz Numbers
• Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers
• 2D Toda $\tau$ Functions, Weighted Hurwitz Numbers and the Cayley Graph: Determinant Representation and Recursion Formula
• Any topological recursion on a rational spectral curve is KP integrable