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A local limit theorem for the critical random graph. (English) Zbl 1185.05129

Summary: We consider the limit distribution of the orders of the \(k\) largest components in the Erdös-Rényi random graph inside the “critical window” for arbitrary \(k\). We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function.

MSC:

05C80 Random graphs (graph-theoretic aspects)
05C35 Extremal problems in graph theory
60C05 Combinatorial probability
60F05 Central limit and other weak theorems
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