On the Fluctuations of the Giant Component

Authors:
D. Barraez;S. Boucheron;W. Fernandez De LaVega
Affiliations:
Departamento de Matematicas, Facultad de Ciencias, Universidad Central de Venezuela, Avenida Los Ilustres, Los Chaguaramos, Caracas, Venezuela (e-mail: dbarraez@euler.ciens.ucv.ve);Laboratoire de Recherche en Informatique, CNRS UMR 8623, Bâtiment 490, Université Paris-sud, 91405 Orsay cedex, France (e-mail: bouchero@lri.fr, lab@lri.fr);Laboratoire de Recherche en Informatique, CNRS UMR 8623, Bâtiment 490, Université Paris-sud, 91405 Orsay cedex, France (e-mail: bouchero@lri.fr, lab@lri.fr)
Venue:
Combinatorics, Probability and Computing
Year:
2000

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Abstract

We provide an alternate proof of the central limit theorem for the uctuations of the size of the giant component in sparse random graphs. In contrast with previous proofs, the argument investigates a depth-first search algorithm, through first-passage analysis using couplings and martingale limit theorems. The analysis of the first passage limiting distribution for sequences of Markov chains might be interesting in its own right. This proof naturally provides an upper bound for the rate of convergence.