Irreversible Aggregation and Network Renormalization

Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the complete solution for the probability to find any given state...

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Bibliographic Details
Published in:arXiv.org 2011-03
Main Authors: Seung-Woo, Son, Bizhani, Golnoosh, Christensen, Claire, Grassberger, Peter, Paczuski, Maya
Format: Article
Language:English
Subjects:
Agglomeration
Percolation
Phase transitions
Scaling laws
Self-similarity
Transportation networks
Online Access:Get full text
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Summary:Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the complete solution for the probability to find any given state in an aggregation process \((k+1)X\to X\), given a fixed number of unit mass particles in the initial state. Exactly the same probability distributions and scaling are found in one dimensional systems (a trivial network) and well-mixed solutions. This reveals that scaling laws found in renormalization of complex networks do not prove that they are self-similar.
ISSN:2331-8422
DOI:10.48550/arxiv.1011.0944