NDLI: Phase Transitions on Markovian Bipartite Graphs—an Application of the Zero-range Process

Content Provider	Springer Nature Link
Author	Pulkkinen, Otto Merikoski, Juha
Copyright Year	2005
Abstract	We analyze the existence and the size of the giant component in the stationary state of a Markovian model for bipartite multigraphs, in which the movement of the edge ends on one set of vertices of the bipartite graph is a zero-range process, the degrees being static on the other set. The analysis is based on approximations by independent variables and on the results of Molloy and Reed for graphs with prescribed degree sequences. The possible types of phase diagrams are identified by studying the behavior below the zero-range condensation point. As a specific example, we consider the so-called Evans interaction. In particular, we examine the values of a critical exponent, describing the growth of the giant component as the value of the dilution parameter controlling the connectivity is increased above the critical threshold. Rigorous analysis spans a large portion of the parameter space of the model exactly at the point of zero-range condensation. These results, supplemented with conjectures supported by Monte Carlo simulations, suggest that the phenomenological Landau theory for percolation on graphs is not broken by the fluctuations.
Starting Page	881
Ending Page	907
Page Count	27
File Format	PDF
ISSN	00224715
Journal	Journal of Statistical Physics
Volume Number	119
Issue Number	3-4
e-ISSN	15729613
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2005-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Random graph giant component zero-range process condensation Physical Chemistry Quantum Physics Mathematical and Computational Physics Statistical Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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