An Asymptotic Expansion for the Number of 2-Connected Chord Diagrams

Abstract

We derive a functional relation between the generating functions of connected chord diagrams and 2-connected chord diagrams. This relation enables us to calculate an asymptotic expansion for the number of 2-connected chord diagrams on $n$ chords. The asymptotic information obtained from this expansion refines the last established results and provides a simple alternative for calculating the asymptotic behaviour of certain Green functions in Quenched QED and Yukawa theory in the context of quantum field theory.

References in corpus (7)

• Hopf Algebras, Renormalization and Noncommutative Geometry
• On Overlapping Divergences
• Hopf algebra approach to Feynman diagram calculations
• Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
• Four-loop Dyson-Schwinger-Johnson anatomy
• Hopf algebraic Renormalization of Kreimer's toy model
• Diffeomorphisms of quantum fields

Cited by in corpus (1)

• Convergence rates of limit theorems in random chord diagrams