Irreversible Aggregation and Network Renormalization

Details Irreversible Aggregation and Network Renormalization Irreversible Aggregation and Network Renormalization

2010-11-03

arxiv.org/abs/1011.0944v2

EPL 95, 58007 (2011)

Physics

Data Analysis, Statistics and Probability

4 pages, 2 figures

Scientific paper

10.1209/0295-5075/95/58007

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.

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