Electronic Communications in Probability

A moment-generating formula for Erdős-Rényi component sizes

Balázs Ráth

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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 [9] and [12] about the susceptibility in the subcritical graph and the CLT [17] for the size of the giant component in the supercritical graph.

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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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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]

Erdős-Rényi graph generating function susceptibility giant component central limit theorem

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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

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