caa a22 4500 467892180 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s10955-006-9101-3 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9101-3 Turova Tatyana Mathematical Center, University of Lund, P.O. Box 118, S-22100, Lund, Sweden aut Phase Transitions in Dynamical Random Graphs [Elektronische Daten] [Tatyana Turova] We study a large-time limit of a Markov process whose states are finite graphs. The number of the vertices is described by a supercritical branching process, and the dynamics of edges is determined by the rates of appending and deleting. We find a phase transition in our model similar to the one in the random graph model G n,p . We derive a formula for the line of critical parameters which separates two different phases: one is where the size of the largest component is proportional to the size of the entire graph, and another one, where the size of the largest component is at most logarithmic with respect to the size of the entire graph. In the supercritical phase we find the asymptotics for the size of the largest component. Springer Science+Business Media, Inc., 2006 inhomogeneous random graphs nationallicence phase transitions nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/5(2006-06-01), 1007-1032 0022-4715 123:5<1007 2006 123 10955 https://doi.org/10.1007/s10955-006-9101-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9101-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Turova Tatyana Mathematical Center, University of Lund, P.O. Box 118, S-22100, Lund, Sweden aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/5(2006-06-01), 1007-1032 0022-4715 123:5<1007 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer