On the largest component of subcritical random hyperbolic graphs

Roland Diel (1) , Dieter Mitsche (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 PSPM - Probabilités, statistique, physique mathématique

We consider the random hyperbolic graph model introduced by [KPK + 10] and then formalized by [GPP12]. We show that, in the subcritical case α > 1, the size of the largest component is n^{1/(2α)+o(1)} , thus strengthening a result of [BFM15] which gave only an upper bound of n^{1/α+o(1)}.

Mots clés: Graph theory; Geometric probability; Random hyperbolic graphs

Domaines: Probabilités [math.PR]

Roland Diel, Dieter Mitsche. On the largest component of subcritical random hyperbolic graphs. Electronic Communications in Probability, 2021, 26 (none), pp.1-14. ⟨10.1214/21-ECP380⟩. ⟨hal-02495492⟩