# $$\hbox {Next-to}{}^k$$ Leading Log Expansions by Chord Diagrams

@article{Courtiel2020hboxL, title={\$\$\hbox \{Next-to\}\{\}^k\$\$ Leading Log Expansions by Chord Diagrams}, author={Julien Courtiel and Karen A. Yeats}, journal={Communications in Mathematical Physics}, year={2020} }

Green functions in a quantum field theory can be expanded as bivariate series in the coupling and a scale parameter. The leading logs are given by the main diagonal of this expansion, i.e. the subseries where the coupling and the scale parameter appear to the same power; then the next-to leading logs are listed by the next diagonal of the expansion, where the power of the coupling is incremented by one, and so on. We give a general method for deriving explicit formulas and asymptotic estimates…

## 10 Citations

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A bijection is described between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorsial maps on the other hand, which naturally extends to indecomposable diagrams and general rooted maps.

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We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We…

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We build on recent work of Yeats, Courtiel, and others involving connected chord diagrams. We first derive from a Hopf-algebraic foundation a class of tree-like functional equations and prove that…

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