Publication : t05/113
Integrability of graph combinatorics via random walks and heaps of dimers
Di Francesco P. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)Guitter E. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Abstract:Année de publication : 2005
We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom trees and is expressed in terms of generating functions for random walks. We construct explicitly an infinite set of conserved quantities for this equation, also involving suitable combinations of random walk generating functions. The proof of their conservation, i.e. their eventual independence on the geodesic distance, relies on the connection between random walks and heaps of dimers. The values of the conserved quantities are identified with generating functions for graphs with fixed numbers of external legs. Alternative equivalent choices for the set of conserved quantities are also discussed and some applications are presented.
Revue : J. Stat. Mech. P09001 (2005)
DOI : 10.1088/1742-5468/2005/09/P09001
Preprint : arXiv:math.CO/0506542
Lien : http://stacks.iop.org/JSTAT/2005/P09001
Keywords : Classical integrability, topology and combinatorics, exact results, random graphs, networks
Langue : Anglais
Fichier(s) à télécharger :
publi.pdf 1742-5468_2005_09_P09001.pdf
