Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 23 (2018), paper no. 24, 14 pp.
A moment-generating formula for Erdős-Rényi component sizes
We derive a simple formula characterizing the distribution of the size of the connected component of a fixed vertex in the Erdős-Rényi random graph which allows us to give elementary proofs of some results of  and  about the susceptibility in the subcritical graph and the CLT  for the size of the giant component in the supercritical graph.
Electron. Commun. Probab., Volume 23 (2018), paper no. 24, 14 pp.
Received: 30 July 2017
Accepted: 12 March 2018
First available in Project Euclid: 26 April 2018
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Digital Object Identifier
Zentralblatt MATH identifier
Primary: 60C05: Combinatorial probability 60F05: Central limit and other weak theorems 82B26: Phase transitions (general) 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
Ráth, Balázs. A moment-generating formula for Erdős-Rényi component sizes. Electron. Commun. Probab. 23 (2018), paper no. 24, 14 pp. doi:10.1214/18-ECP126. https://projecteuclid.org/euclid.ecp/1524708114