Laplace transform of the $x-y$ symplectic transformation formula in Topological Recursion
Alexander Hock
Abstract
The functional relation coming from the xy symplectic transformation of Topological Recursion has a lot of applications, for instance it is the higher order moment-cumulant relation in free probability or can be used to compute intersection numbers on the moduli space of complex curves.We derive the Laplace transform of this functional relation, which has a very nice and compact form as a formal power series in .We apply the Laplace transformed formula to the Airy curve and the Lambert curve.
Topics & Concepts
Symplectic geometryMathematicsLaplace transformTransformation (genetics)Recursion (computer science)Pure mathematicsTopology (electrical circuits)Mathematical analysisCombinatoricsAlgorithmBiochemistryGeneChemistryAlgebraic and Geometric Analysisadvanced mathematical theories