Projects per year

### Abstract

We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We give a criterion for the existence of a giant component, which is both necessary and sufficient, and which becomes explicit when f is linear. Otherwise it allows the derivation of explicit necessary and sufficient conditions, which are often fairly close. We give an explicit criterion to decide whether the giant component is robust under random removal of edges. We also determine asymptotically the size of the giant component and the empirical distribution of component sizes in terms of the survival probability and size distribution of a multitype branching random walk associated with f.

Original language | English |
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Pages (from-to) | 329-384 |

Number of pages | 56 |

Journal | Annals of Probability |

Volume | 41 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2013 |

## Fingerprint Dive into the research topics of 'Random networks with sublinear preferential attachment: the giant component'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA

Morters, P.

Engineering and Physical Sciences Research Council

1/09/05 → 31/08/10

Project: Research council

## Cite this

Dereich, S., & Morters, P. (2013). Random networks with sublinear preferential attachment: the giant component.

*Annals of Probability*,*41*(1), 329-384. https://doi.org/10.1214/11-AOP697