We consider the random hyperbolic graph model introduced by [KPK+10] and then formalized by [GPP12]. We show that, in the subcritical case , the size of the largest component is asymptotically almost surely , thus strengthening a result of [BFM15] which gave only an upper bound of .
Roland Diel has been partially supported by grant GrHyDy ANR-20-CE40-0002. Dieter Mitsche has been partially supported by grant GrHyDy ANR-20-CE40-0002 and by IDEXLYON of Université de Lyon (Programme Investissements d’Avenir ANR16-IDEX-0005).
The authors would like to thank Antoine Barrier for providing Figure 1 and the anonymous referees for their many valuable comments which helped to significantly improve the clarity of the paper.
"On the largest component of subcritical random hyperbolic graphs." Electron. Commun. Probab. 26 1 - 14, 2021. https://doi.org/10.1214/21-ECP380