Arkiv för Matematik

  • Ark. Mat.
  • Volume 51, Number 2 (2013), 371-403.

Asymptotics for the size of the largest component scaled to “logn” in inhomogeneous random graphs

Tatyana S. Turova

Full-text: Open access

Abstract

We study inhomogeneous random graphs in the subcritical case. Among other results, we derive an exact formula for the size of the largest connected component scaled by log n, with n being the size of the graph. This generalizes a result for the “rank-1 case”. We also investigate branching processes associated with these graphs. In particular, we discover that the same well-known equation for the survival probability, whose positive solution determines the asymptotics of the size of the largest component in the supercritical case, also plays a crucial role in the subcritical case. However, now it is the negative solutions that come into play. We disclose their relationship to the distribution of the progeny of the branching process.

Note

This research was supported by the Swedish Research Council.

Article information

Source
Ark. Mat., Volume 51, Number 2 (2013), 371-403.

Dates
Received: 11 January 2012
First available in Project Euclid: 1 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907222

Digital Object Identifier
doi:10.1007/s11512-012-0178-4

Mathematical Reviews number (MathSciNet)
MR3090203

Zentralblatt MATH identifier
1270.05091

Rights
2012 © Institut Mittag-Leffler

Citation

Turova, Tatyana S. Asymptotics for the size of the largest component scaled to “log n ” in inhomogeneous random graphs. Ark. Mat. 51 (2013), no. 2, 371--403. doi:10.1007/s11512-012-0178-4. https://projecteuclid.org/euclid.afm/1485907222


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