Irreversible Aggregation and Network Renormalization

Abstract

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.

4 pages, 2 figures

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• Random Sequential Renormalization and Agglomerative Percolation in Networks: Application to Erd"os-R'enyi and Scale-free Graphs
• Exact combinatorial approach to finite coagulating systems through recursive equations
• Combinatorial solutions to generalized electrorheological kernel aggregation
• Coalescense with arbitrary-parameter kernels and monodisperse initial conditions: A study within combinatorial framework