Phase Transition in a Generalized Eden Growth Model on a Tree - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Statistical Physics Année : 2006

Phase Transition in a Generalized Eden Growth Model on a Tree

Résumé

We study analytically the late time statistics of the number of particles in an Eden growth model on a tree. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by absorbing new particles at the empty perimeter sites at a rate proportional to c −l where c is a positive parameter and l is the distance of the perimeter site from the root. For c=1, this model corresponds to random binary search trees and for c=2 it corresponds to digital search trees in computer science. By introducing a backward Fokker-Planck approach, we calculate the mean and the variance of the number of particles at large times and show that the variance undergoes a 'phase transition' at a critical value . While for the variance is proportional to the mean and the distribution is normal, for the variance is anomalously large and the distribution is non-Gaussian due to the appearance of extreme fluctuations. The model is generalized to one where growth occurs on a tree with m branches and, in this more general case, we show that the critical point occurs at .

Dates et versions

hal-00116755 , version 1 (27-11-2006)

Identifiants

Citer

David S. Dean, Satya N. Majumdar. Phase Transition in a Generalized Eden Growth Model on a Tree. Journal of Statistical Physics, 2006, 124, pp.1351-1376. ⟨10.1007/s10955-006-9193-9⟩. ⟨hal-00116755⟩
62 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More