Rooted Tree Graphs and the Butcher Group: Combinatorics of Elementary Perturbation Theory

DOI10.1007/978-981-15-0298-9_6zbMath1446.82035arXiv2101.09364OpenAlexW2980695522MaRDI QIDQ3296398

William G. Faris

Publication date: 7 July 2020

Published in: Sojourns in Probability Theory and Statistical Physics - II (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.09364

zbMATH Keywords

perturbation expansioncombinatorial speciesButcher grouprooted tree graphsHopf algebras of treesConnes-Kreimer renormalization

Mathematics Subject Classification ID

Trees (05C05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Renormalization group methods in equilibrium statistical mechanics (82B28) Percolation (82B43)

Related Items (1)

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Cites Work

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• The Lie group structure of the Butcher group
• Two interacting Hopf algebras of trees: a Hopf-algebraic approach to composition and substitution of B-series.
• Combinatorial species and Feynman diagrams
• Multistep-multistage-multiderivative methods for ordinary differential equations
• Combinatorics and cluster expansions
• On the Butcher group and general multi-value methods
• Hopf algebras, renormalization and noncommutative geometry
• Applied finite group actions.
• Algebraic structures of B-series
• An algebraic Birkhoff decomposition for the continuous renormalization group
• An Algebraic Theory of Integration Methods

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