caa a22 4500 467891265 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060901xx s 000 0 eng 10.1007/s10955-006-9193-9 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9193-9 Phase Transition in a Generalized Eden Growth Model on a Tree [Elektronische Daten] [David Dean, Satya Majumdar] 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 $$c=\sqrt{2}$$ . While for $$c>\sqrt{2}$$ the variance is proportional to the mean and the distribution is normal, for $$c<\sqrt{2}$$ 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 $$c=\sqrt{m}$$ . Springer Science + Business Media, Inc., 2006 Search trees nationallicence Growth models nationallicence Phase transitions nationallicence Dean David Laboratoire de Physique Théorique, UMR CNRS 5152, IRSAMC, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 04, France aut Majumdar Satya Laboratoire de Physique Théorique et Modéles Statistiques, UMR CNRS 8626, Université Paris Sud, Bât 100, 91045, Orsay Cedex, France aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/6(2006-09-01), 1351-1376 0022-4715 124:6<1351 2006 124 10955 https://doi.org/10.1007/s10955-006-9193-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9193-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dean David Laboratoire de Physique Théorique, UMR CNRS 5152, IRSAMC, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 04, France aut NATIONALLICENCE 700 1- Majumdar Satya Laboratoire de Physique Théorique et Modéles Statistiques, UMR CNRS 8626, Université Paris Sud, Bât 100, 91045, Orsay Cedex, France aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/6(2006-09-01), 1351-1376 0022-4715 124:6<1351 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer