Van Der Hofstad, Remco W.; Kager, Wouter; Müller, Tobias A local limit theorem for the critical random graph. (English) Zbl 1185.05129 Electron. Commun. Probab. 14, 122-131 (2009). 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. Cited in 7 Documents MSC: 05C80 Random graphs (graph-theoretic aspects) 05C35 Extremal problems in graph theory 60C05 Combinatorial probability 60F05 Central limit and other weak theorems Keywords:ERdoes-Renyi random graphs; local limit theorem PDFBibTeX XMLCite \textit{R. W. Van Der Hofstad} et al., Electron. Commun. Probab. 14, 122--131 (2009; Zbl 1185.05129) Full Text: DOI EuDML EMIS