The Average Size of Giant Components Between the Double-Jump
<|reference_start|>The Average Size of Giant Components Between the Double-Jump: We study the sizes of connected components according to their excesses during a random graph process built with $n$ vertices. The considered model is the continuous one defined in Janson 2000. An ${\ell}$-component is a connected component with ${\ell}$ edges more than vertices. $\ell$ is also called the \textit{excess} of such component. As our main result, we show that when $\ell$ and ${n \over \ell}$ are both large, the expected number of vertices that ever belong to an $\ell$-component is about ${12}^{1/3} {\ell}^{1/3} n^{2/3}$. We also obtain limit theorems for the number of creations of $\ell$-components.<|reference_end|>
@article{ravelomanana2006the,
    title={The Average Size of Giant Components Between the Double-Jump},
    author={Vlady Ravelomanana (LIPN), the Projet PAI Amadeus Collaboration},
    journal={Algorithmica Issue sp\'{e}ciale "Analysis of Algorithms" (2006) A
  para\^{i}tre},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0607057},
    primaryClass={cs.DM math.CO math.PR}
}