Mesoscopic scales in hierarchical configuration models

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademic

73 Downloads (Pure)

Samenvatting

To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. The connections between the communities are formed as in a configuration model. We study the component sizes of the hierarchical configuration model at criticality when the inter-community degrees have a finite third moment. We find the conditions on the community sizes such that the critical component sizes of the HCM behave similarly as in the configuration model. Furthermore, we study critical bond percolation on the HCM. We show that the ordered components of a critical HCM on $N$ vertices are of sizes $O(N^{2/3})$. More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift, as for the scaling limit for the configuration model under a finite third moment condition.
Originele taal-2Engels
Artikelnummer1612.02668
Aantal pagina's27
TijdschriftarXiv
Nummer van het tijdschrift1612.02668
StatusGepubliceerd - 8 dec 2016

Trefwoorden

  • math.PR

Vingerafdruk Duik in de onderzoeksthema's van 'Mesoscopic scales in hierarchical configuration models'. Samen vormen ze een unieke vingerafdruk.

Citeer dit