Terminal chords in connected chord diagrams - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions Année : 2017

Terminal chords in connected chord diagrams

Résumé

Rooted connected chord diagrams form a nice class of combinatorial objects. Recently they were shown to index solutions to certain Dyson-Schwinger equations in quantum field theory. Key to this indexing role are certain special chords which are called terminal chords. Terminal chords provide a number of combinatorially interesting parameters on rooted connected chord diagrams which have not been studied previously. Understanding these parameters better has implications for quantum field theory. Specifically, we show that the distributions of the number of terminal chords and the number of adjacent terminal chords are asymptotically Gaus-sian with logarithmic means, and we prove that the average index of the first terminal chord is 2n/3. Furthermore, we obtain a method to determine any next-to i leading log expansion of the solution to these Dyson-Schwinger equations, and have asymptotic information about the coefficients of the log expansions.
Fichier principal
Vignette du fichier
terminal chords_revision.pdf (489.23 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01653711 , version 1 (01-12-2017)

Identifiants

Citer

Julien Courtiel, Karen Yeats. Terminal chords in connected chord diagrams. Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2017, 4 (4), pp.417-452. ⟨10.4171/AIHPD/44⟩. ⟨hal-01653711⟩
336 Consultations
201 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More