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Emergence of the giant component in special Marcus-Lushnikov processes. (English) Zbl 1002.60564
Summary: Component sizes in the usual random graph process are a special case of the Marcus-Lushnikov process discussed in the scientific literature, so it is natural to ask how theory surrounding emergence of the giant component generalizes to the Marcus-Lushnikov process. Essentially no rigorous results are known; we make a start by proving a weak result, but our main purpose is to draw this topic to the attention of random graph theorists.

MSC:
60J27 Continuous-time Markov processes on discrete state spaces
05C80 Random graphs (graph-theoretic aspects)
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