Publication : t06/186
Mass distribution exponents for growing trees
David F. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)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)
Jonsson T. (Science Institute, Universily of Iceland Dunhaga 3, 107, Reykjavik, ICELAND)
Abstract:Année de publication : 2007
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that measures the repartition of the mass of large trees between their different subtrees. This distribution is shown to be a broad distribution and we derive explicit expressions for scaling exponents that characterize its behavior when one subtree is much smaller than the others. We show in particular the existence of various regimes with different values of these mass distribution exponents. Our results are corroborated by a number of exact solutions for particular solvable cases, as well as by numerical simulations.
Revue : J. Stat. Mech. P02011 (2007)
DOI : 10.1088/1742-5468/2007/02/P02011
Preprint : arXiv:cond-mat/0612412
Lien : http://stacks.iop.org/JSTAT/2007/P02011
PACS : 05.90.+m , 02.50.Ey , 02.70.Rr ,
Keywords : cond-mat Subj-class: Statistical Mechanics. growth processes; trees; scaling exponents
Langue : Anglais
Fichier(s) à télécharger :
1742-5468_2007_02_P02011.pdf publi.pdf
